I am observing the same issue on a Toshiba Satelite A110 laptop. It has the following video card:
andrew@sat11:~$ lspci | grep Graphics
00:02.0 VGA compatible controller: Intel Corporation Mobile 945GM/GMS, 943/940GML Express Integrated Graphics Controller (rev 03)
00:02.1 Display controller: Intel Corporation Mobile 945GM/GMS/GME, 943/940GML Express Integrated Graphics Controller (rev 03)

OpenGL games (testing with Supertux and Nexuiz) get distorted if desktop effects are enabled. If effects are disabled everything is ok. Playing the games in full screen or in windowed mode makes no difference.

When starting a opengl game with desktop effects enabled distortion does not happen at once. For a couple of seconds after starting the game all looks as normal. Then some elements disappear from screen and the rest get distorted.

On the other hand I am using the GLmatrix screensaver on this laptop, and I believe it uses openGL too. I have never had such issues with the screensaver.

Here's a list of the packages that seem relevant to me, along with their versions:
andrew@sat11:~$ dpkg -l | grep -i opengl
ii  compiz                                    1:0.7.8-0ubuntu4.1                    OpenGL window and compositing manager
ii  compiz-core                               1:0.7.8-0ubuntu4.1                    OpenGL window and compositing manager
ii  compiz-gnome                              1:0.7.8-0ubuntu4.1                    OpenGL window and compositing manager - GNOM
ii  compiz-plugins                            1:0.7.8-0ubuntu4.1                    OpenGL window and compositing manager - plug
ii  compiz-wrapper                            1:0.7.8-0ubuntu4.1                    OpenGL window and compositing manager, wrapp
ii  freeglut3                                 2.4.0-6.1                             OpenGL Utility Toolkit
ii  libgl1-mesa-dri                           7.2-1ubuntu2                          A free implementation of the OpenGL API -- D
ii  libgl1-mesa-glx                           7.2-1ubuntu2                          A free implementation of the OpenGL API -- G
ii  libglew1.5                                1.5.0dfsg1-3ubuntu1                   The OpenGL Extension Wrangler - runtime envi
ii  libglitz-glx1                             0.5.6-1                               Glitz OpenGL library GLX backend
ii  libglitz1                                 0.5.6-1                               Glitz OpenGL image compositing library
ii  libglu1-mesa                              7.2-1ubuntu2                          The OpenGL utility library (GLU)
ii  libglut3                                  3.7-25                                the OpenGL Utility Toolkit
ii  libgtkglext1                              1.2.0-1ubuntu1                        OpenGL Extension to GTK+ (shared libraries)
ii  libqt4-opengl                             4.4.3-0ubuntu1                        Qt 4 OpenGL module
andrew@sat11:~$ dpkg -l | grep -i supertux
ii  supertux                                  0.3.1d-0ubuntu2                       Classic 2D jump 'n run sidescroller with Tux
ii  supertux-data                             0.3.1d-0ubuntu2                       Levels for classic 2D jump 'n run sidescroll
andrew@sat11:~$ dpkg -l | grep -i nexuiz
ii  nexuiz                                    2.4.2-1                               A fast-paced 3D first-person shooter
ii  nexuiz-data                               2.4.2-1                               Nexuiz game data files
ii  nexuiz-music                              2.4.2-1                               Nexuiz music files

Please advise if other information is needed.