Turok 2 will crash in Hi-Res mode from overheating the N64. And the Turok 2 demo for PC only worked on a very narrow set of hardware, everything else would lock up the PC.
Mario 64 will crash if you manage to fall out of the game world when doing one of the door-skip glitches (like the bunny one, or the long-jump in reverse one)
I think everyone remembers the MISSINGNO Pokemon glitch, and what would happen if you captured it then saved
Mario Kart 64 had a few places where you could fall out of the game world and it'd lock up (other places would just act like you fell in water and Lakitu would pick you up).
There's quite a few games with insanely "touchy" CD protection software, including UT2003 (or was it 04?). UT2003 released a patch soon after that would allow you to play without the CD in the drive.
Diablo II likes to crash on the latest patch if it can't access your cinematics (either cause you opted for the CD method or what have you).