MSR on the Dreamcast was a fun one. The original release being so bugged that Sega did a recall (at least in PAL ter.).
The game like project gotham required you to get a certain amount of Kudos before getting to the next level. The original version didn't seem to care, it just kept unlocking everything. Also on the press start screen, if you were using VGA and left it for too long the screen would go grey and you'd have to restart the dreamcast.
I think there was a buffer overflow every now and again as the accelerometer would get screwed up and your car would suddenly be doing a speed that could only be displayed in scientific formular. On the screen would be the car and just black space.
Still that game was awesome...
The auto demo that came out long before had a helpful bug too. If you had a second controller plugged in, and held a button down it never turned off. I remember my mum walking in and plonking a load of washing ontop of the controller while I was watching the demo. I sat there for ages just watching that demo lol :)