No textures render at all, period. The ground is invisible, but tunnels can be seen if they are dug. The trees, the only things visible at start, are solid black, both trunks and leaves. When blocks are placed, they are solid black as well. Digging causes a solid black shape of the removed cube to appear. Some blocks, like signs, don't even appear at all. Water does not show up. The audio, however, is completely fine. The physics also appear to be functioning.

In order to reproduce the bug, I simply need to start Minecraft. It happens every time.

I forced a crash; the crash log is attached. The client log is also included. Of note is the indication that the "vertex program could not be created." Perhaps my system is just too outdated. It does appear to support OpenGL 2.0, though.
While there are similar problems reported here, I have an entirely different GPU/display adapter than the other ATI ones.