Same problem here. MTU of the server is 1500, changing client MTU to the same value doesn't fix it. 

Testing with ping, 1300 byte pings make it through fine, so tried setting client MTU to that on both client and server. No dice.

Server version is OpenSSH_5.9p1 Debian-5ubuntu1.4, OpenSSL 1.0.1 14 Mar 2012.
A client running OpenSSH_5.3p1, OpenSSL 1.0.1e-fips 11 Feb 2013 can connect.
A client running OpenSSH_6.6.1p1 Ubuntu-2ubuntu2, OpenSSL 1.0.1f 6 Jan 2014 *cannot* connect.

Successful connection:

% ssh -vv [redacted]
OpenSSH_5.3p1, OpenSSL 1.0.1e-fips 11 Feb 2013
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: Applying options for *
debug2: ssh_connect: needpriv 0
debug1: Connecting to [redacted] port 22.
debug1: Connection established.
debug1: identity file /home/meta/.ssh/identity type -1
debug1: identity file /home/meta/.ssh/identity-cert type -1
debug1: identity file /home/meta/.ssh/id_rsa type -1
debug1: identity file /home/meta/.ssh/id_rsa-cert type -1
debug1: identity file /home/meta/.ssh/id_dsa type -1
debug1: identity file /home/meta/.ssh/id_dsa-cert type -1
debug1: Remote protocol version 2.0, remote software version OpenSSH_5.9p1 Debian-5ubuntu1.4
debug1: match: OpenSSH_5.9p1 Debian-5ubuntu1.4 pat OpenSSH*
debug1: Enabling compatibility mode for protocol 2.0
debug1: Local version string SSH-2.0-OpenSSH_5.3
debug2: fd 3 setting O_NONBLOCK
debug1: SSH2_MSG_KEXINIT sent
debug1: SSH2_MSG_KEXINIT received
debug2: kex_parse_kexinit: diffie-hellman-group-exchange-sha256,diffie-hellman-group-exchange-sha1,diffie-hellman-group14-sha1,diffie-hellman-group1-sha1
debug2: kex_parse_kexinit: <email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,ssh-rsa,ssh-dss
debug2: kex_parse_kexinit: aes128-ctr,aes192-ctr,aes256-ctr,arcfour256,arcfour128,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,<email address hidden>
debug2: kex_parse_kexinit: aes128-ctr,aes192-ctr,aes256-ctr,arcfour256,arcfour128,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,<email address hidden>
debug2: kex_parse_kexinit: hmac-md5,hmac-sha1,<email address hidden>,hmac-sha2-256,hmac-sha2-512,hmac-ripemd160,<email address hidden>,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: hmac-md5,hmac-sha1,<email address hidden>,hmac-sha2-256,hmac-sha2-512,hmac-ripemd160,<email address hidden>,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: none,<email address hidden>,zlib
debug2: kex_parse_kexinit: none,<email address hidden>,zlib
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: first_kex_follows 0 
debug2: kex_parse_kexinit: reserved 0 
debug2: kex_parse_kexinit: ecdh-sha2-nistp256,ecdh-sha2-nistp384,ecdh-sha2-nistp521,diffie-hellman-group-exchange-sha256,diffie-hellman-group-exchange-sha1,diffie-hellman-group14-sha1,diffie-hellman-group1-sha1
debug2: kex_parse_kexinit: ssh-rsa,ssh-dss,ecdsa-sha2-nistp256
debug2: kex_parse_kexinit: aes128-ctr,aes192-ctr,aes256-ctr,arcfour256,arcfour128,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,<email address hidden>
debug2: kex_parse_kexinit: aes128-ctr,aes192-ctr,aes256-ctr,arcfour256,arcfour128,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,<email address hidden>
debug2: kex_parse_kexinit: hmac-md5,hmac-sha1,<email address hidden>,hmac-sha2-256,hmac-sha2-256-96,hmac-sha2-512,hmac-sha2-512-96,hmac-ripemd160,<email address hidden>,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: hmac-md5,hmac-sha1,<email address hidden>,hmac-sha2-256,hmac-sha2-256-96,hmac-sha2-512,hmac-sha2-512-96,hmac-ripemd160,<email address hidden>,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: none,<email address hidden>
debug2: kex_parse_kexinit: none,<email address hidden>
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: first_kex_follows 0 
debug2: kex_parse_kexinit: reserved 0 
debug2: mac_setup: found hmac-md5
debug1: kex: server->client aes128-ctr hmac-md5 none
debug2: mac_setup: found hmac-md5
debug1: kex: client->server aes128-ctr hmac-md5 none
debug1: SSH2_MSG_KEX_DH_GEX_REQUEST(1024<1024<8192) sent
debug1: expecting SSH2_MSG_KEX_DH_GEX_GROUP
debug2: dh_gen_key: priv key bits set: 126/256
debug2: bits set: 496/1024
debug1: SSH2_MSG_KEX_DH_GEX_INIT sent
debug1: expecting SSH2_MSG_KEX_DH_GEX_REPLY
debug1: Host '[redacted]' is known and matches the RSA host key.
debug1: Found key in /home/meta/.ssh/known_hosts:3
debug2: bits set: 487/1024
debug1: ssh_rsa_verify: signature correct
debug2: kex_derive_keys
debug2: set_newkeys: mode 1
debug1: SSH2_MSG_NEWKEYS sent
debug1: expecting SSH2_MSG_NEWKEYS
debug2: set_newkeys: mode 0
debug1: SSH2_MSG_NEWKEYS received
debug1: SSH2_MSG_SERVICE_REQUEST sent
debug2: service_accept: ssh-userauth
debug1: SSH2_MSG_SERVICE_ACCEPT received
debug2: key: /home/meta/.ssh/identity ((nil))
debug2: key: /home/meta/.ssh/id_rsa ((nil))
debug2: key: /home/meta/.ssh/id_dsa ((nil))
debug1: Authentications that can continue: publickey,gssapi-keyex,gssapi-with-mic,password
debug1: Next authentication method: gssapi-keyex
debug1: No valid Key exchange context
debug2: we did not send a packet, disable method
debug1: Next authentication method: gssapi-with-mic
debug1: Unspecified GSS failure.  Minor code may provide more information
Cannot determine realm for numeric host address
debug1: Unspecified GSS failure.  Minor code may provide more information
Cannot determine realm for numeric host address
debug1: Unspecified GSS failure.  Minor code may provide more information
debug1: Unspecified GSS failure.  Minor code may provide more information
Cannot determine realm for numeric host address
debug2: we did not send a packet, disable method
debug1: Next authentication method: publickey
debug1: Trying private key: /home/meta/.ssh/identity
debug1: Trying private key: /home/meta/.ssh/id_rsa
debug1: Trying private key: /home/meta/.ssh/id_dsa
debug2: we did not send a packet, disable method
debug1: Next authentication method: password

Failed connection:

% ssh -vv [redacted]
OpenSSH_6.6.1, OpenSSL 1.0.1f 6 Jan 2014
debug1: Reading configuration data /home/meta/.ssh/config
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: /etc/ssh/ssh_config line 19: Applying options for *
debug2: ssh_connect: needpriv 0
debug1: Connecting to [redacted] port 22.
debug1: Connection established.
debug1: identity file /home/meta/.ssh/id_rsa type 1
debug1: identity file /home/meta/.ssh/id_rsa-cert type -1
debug1: identity file /home/meta/.ssh/id_dsa type -1
debug1: identity file /home/meta/.ssh/id_dsa-cert type -1
debug1: identity file /home/meta/.ssh/id_ecdsa type -1
debug1: identity file /home/meta/.ssh/id_ecdsa-cert type -1
debug1: identity file /home/meta/.ssh/id_ed25519 type -1
debug1: identity file /home/meta/.ssh/id_ed25519-cert type -1
debug1: Enabling compatibility mode for protocol 2.0
debug1: Local version string SSH-2.0-OpenSSH_6.6.1p1 Ubuntu-2ubuntu2
debug1: Remote protocol version 2.0, remote software version OpenSSH_5.9p1 Debian-5ubuntu1.4
debug1: match: OpenSSH_5.9p1 Debian-5ubuntu1.4 pat OpenSSH_5* compat 0x0c000000
debug2: fd 3 setting O_NONBLOCK
debug1: SSH2_MSG_KEXINIT sent
debug1: SSH2_MSG_KEXINIT received
debug2: kex_parse_kexinit: <email address hidden>,ecdh-sha2-nistp256,ecdh-sha2-nistp384,ecdh-sha2-nistp521,diffie-hellman-group-exchange-sha256,diffie-hellman-group-exchange-sha1,diffie-hellman-group14-sha1,diffie-hellman-group1-sha1
debug2: kex_parse_kexinit: <email address hidden>,<email address hidden>,ssh-rsa,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,ecdsa-sha2-nistp256,ecdsa-sha2-nistp384,ecdsa-sha2-nistp521,ssh-ed25519,ssh-dss
debug2: kex_parse_kexinit: aes128-ctr,aes192-ctr,aes256-ctr,arcfour256,arcfour128,<email address hidden>,<email address hidden>,<email address hidden>,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,<email address hidden>
debug2: kex_parse_kexinit: aes128-ctr,aes192-ctr,aes256-ctr,arcfour256,arcfour128,<email address hidden>,<email address hidden>,<email address hidden>,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,<email address hidden>
debug2: kex_parse_kexinit: <email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,hmac-md5,hmac-sha1,<email address hidden>,<email address hidden>,hmac-sha2-256,hmac-sha2-512,hmac-ripemd160,<email address hidden>,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: <email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,hmac-md5,hmac-sha1,<email address hidden>,<email address hidden>,hmac-sha2-256,hmac-sha2-512,hmac-ripemd160,<email address hidden>,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: none,<email address hidden>,zlib
debug2: kex_parse_kexinit: none,<email address hidden>,zlib
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: first_kex_follows 0 
debug2: kex_parse_kexinit: reserved 0 
debug2: kex_parse_kexinit: ecdh-sha2-nistp256,ecdh-sha2-nistp384,ecdh-sha2-nistp521,diffie-hellman-group-exchange-sha256,diffie-hellman-group-exchange-sha1,diffie-hellman-group14-sha1,diffie-hellman-group1-sha1
debug2: kex_parse_kexinit: ssh-rsa,ssh-dss,ecdsa-sha2-nistp256
debug2: kex_parse_kexinit: aes128-ctr,aes192-ctr,aes256-ctr,arcfour256,arcfour128,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,<email address hidden>
debug2: kex_parse_kexinit: aes128-ctr,aes192-ctr,aes256-ctr,arcfour256,arcfour128,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,<email address hidden>
debug2: kex_parse_kexinit: hmac-md5,hmac-sha1,<email address hidden>,hmac-sha2-256,hmac-sha2-256-96,hmac-sha2-512,hmac-sha2-512-96,hmac-ripemd160,<email address hidden>,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: hmac-md5,hmac-sha1,<email address hidden>,hmac-sha2-256,hmac-sha2-256-96,hmac-sha2-512,hmac-sha2-512-96,hmac-ripemd160,<email address hidden>,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: none,<email address hidden>
debug2: kex_parse_kexinit: none,<email address hidden>
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: first_kex_follows 0 
debug2: kex_parse_kexinit: reserved 0 
debug2: mac_setup: setup hmac-md5
debug1: kex: server->client aes128-ctr hmac-md5 none
debug2: mac_setup: setup hmac-md5
debug1: kex: client->server aes128-ctr hmac-md5 none
debug1: sending SSH2_MSG_KEX_ECDH_INIT
debug1: expecting SSH2_MSG_KEX_ECDH_REPLY
[locks up]

What's weirder is that I have another server running Ubuntu 12.02LTS, and that one responds fine. Transcript from SSH to that system:

meta@w510 % ssh -vv [redacted]
OpenSSH_6.6.1, OpenSSL 1.0.1f 6 Jan 2014
debug1: Reading configuration data /home/meta/.ssh/config
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: /etc/ssh/ssh_config line 19: Applying options for *
debug2: ssh_connect: needpriv 0
debug1: Connecting to [redacted] port 22.
debug1: Connection established.
debug1: identity file /home/meta/.ssh/id_rsa type 1
debug1: identity file /home/meta/.ssh/id_rsa-cert type -1
debug1: identity file /home/meta/.ssh/id_dsa type -1
debug1: identity file /home/meta/.ssh/id_dsa-cert type -1
debug1: identity file /home/meta/.ssh/id_ecdsa type -1
debug1: identity file /home/meta/.ssh/id_ecdsa-cert type -1
debug1: identity file /home/meta/.ssh/id_ed25519 type -1
debug1: identity file /home/meta/.ssh/id_ed25519-cert type -1
debug1: Enabling compatibility mode for protocol 2.0
debug1: Local version string SSH-2.0-OpenSSH_6.6.1p1 Ubuntu-2ubuntu2
debug1: Remote protocol version 2.0, remote software version OpenSSH_5.9p1 Debian-5ubuntu1.4
debug1: match: OpenSSH_5.9p1 Debian-5ubuntu1.4 pat OpenSSH_5* compat 0x0c000000
debug2: fd 3 setting O_NONBLOCK
debug1: SSH2_MSG_KEXINIT sent
debug1: SSH2_MSG_KEXINIT received
debug2: kex_parse_kexinit: <email address hidden>,ecdh-sha2-nistp256,ecdh-sha2-nistp384,ecdh-sha2-nistp521,diffie-hellman-group-exchange-sha256,diffie-hellman-group-exchange-sha1,diffie-hellman-group14-sha1,diffie-hellman-group1-sha1
debug2: kex_parse_kexinit: <email address hidden>,<email address hidden>,ssh-rsa,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,ecdsa-sha2-nistp256,ecdsa-sha2-nistp384,ecdsa-sha2-nistp521,ssh-ed25519,ssh-dss
debug2: kex_parse_kexinit: aes128-ctr,aes192-ctr,aes256-ctr,arcfour256,arcfour128,<email address hidden>,<email address hidden>,<email address hidden>,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,<email address hidden>
debug2: kex_parse_kexinit: aes128-ctr,aes192-ctr,aes256-ctr,arcfour256,arcfour128,<email address hidden>,<email address hidden>,<email address hidden>,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,<email address hidden>
debug2: kex_parse_kexinit: <email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,hmac-md5,hmac-sha1,<email address hidden>,<email address hidden>,hmac-sha2-256,hmac-sha2-512,hmac-ripemd160,<email address hidden>,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: <email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,<email address hidden>,hmac-md5,hmac-sha1,<email address hidden>,<email address hidden>,hmac-sha2-256,hmac-sha2-512,hmac-ripemd160,<email address hidden>,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: none,<email address hidden>,zlib
debug2: kex_parse_kexinit: none,<email address hidden>,zlib
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: first_kex_follows 0 
debug2: kex_parse_kexinit: reserved 0 
debug2: kex_parse_kexinit: ecdh-sha2-nistp256,ecdh-sha2-nistp384,ecdh-sha2-nistp521,diffie-hellman-group-exchange-sha256,diffie-hellman-group-exchange-sha1,diffie-hellman-group14-sha1,diffie-hellman-group1-sha1
debug2: kex_parse_kexinit: ssh-rsa,ssh-dss,ecdsa-sha2-nistp256
debug2: kex_parse_kexinit: aes128-ctr,aes192-ctr,aes256-ctr,arcfour256,arcfour128,arcfour
debug2: kex_parse_kexinit: aes128-ctr,aes192-ctr,aes256-ctr,arcfour256,arcfour128,arcfour
debug2: kex_parse_kexinit: hmac-sha1,hmac-ripemd160
debug2: kex_parse_kexinit: hmac-sha1,hmac-ripemd160
debug2: kex_parse_kexinit: none,<email address hidden>
debug2: kex_parse_kexinit: none,<email address hidden>
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: first_kex_follows 0 
debug2: kex_parse_kexinit: reserved 0 
debug2: mac_setup: setup hmac-sha1
debug1: kex: server->client aes128-ctr hmac-sha1 none
debug2: mac_setup: setup hmac-sha1
debug1: kex: client->server aes128-ctr hmac-sha1 none
debug1: sending SSH2_MSG_KEX_ECDH_INIT
debug1: expecting SSH2_MSG_KEX_ECDH_REPLY
debug1: Server host key: RSA d1:cb:3e:bf:8a:b1:f2:44:22:14:66:84:be:c2:c1:89
debug1: Host '[redacted]' is known and matches the RSA host key.
debug1: Found key in /home/meta/.ssh/known_hosts:7
debug1: ssh_rsa_verify: signature correct
debug2: kex_derive_keys
debug2: set_newkeys: mode 1
debug1: SSH2_MSG_NEWKEYS sent
debug1: expecting SSH2_MSG_NEWKEYS
debug2: set_newkeys: mode 0
debug1: SSH2_MSG_NEWKEYS received
debug1: Roaming not allowed by server
debug1: SSH2_MSG_SERVICE_REQUEST sent
debug2: service_accept: ssh-userauth
debug1: SSH2_MSG_SERVICE_ACCEPT received
debug2: key: /home/meta/.ssh/id_rsa (0x7ff0476f2460),
debug2: key: /home/meta/.ssh/id_dsa ((nil)),
debug2: key: /home/meta/.ssh/id_ecdsa ((nil)),
debug2: key: /home/meta/.ssh/id_ed25519 ((nil)),
debug1: Authentications that can continue: publickey,gssapi-keyex,gssapi-with-mic,password
debug1: Next authentication method: publickey
debug1: Offering RSA public key: /home/meta/.ssh/id_rsa
debug2: we sent a publickey packet, wait for reply
debug1: Server accepts key: pkalg ssh-rsa blen 279
debug2: input_userauth_pk_ok: fp e5:2c:d4:f8:4f:63:c3:ab:e7:ac:10:5e:84:ee:40:60
debug1: key_parse_private2: missing begin marker
debug1: key_parse_private_pem: PEM_read_PrivateKey failed
debug1: read PEM private key done: type <unknown>
[etc]

I also have other non-Ubuntu servers behind the same VPN, and they respond fine. So it's some strange interaction of SSH versions, protocols, and the VPN.