From what I can tell, the CPU karts in Super Mario Kart basically aren't bound by the same laws of physics as the player's kart. They seem to turn without drifting without slowing down, blast me off the road even though I'm pretty sure I'm heavier than they are, and drive right through a road completely blocked by Thwomps. I'm aware that they cheat to make things challenging (which I'm fine with if it's not blatent, which it is), but this kind of stuff seems too cheap to be true, and given that I see myself driving through pipes sometimes I'm not sure what's up. Are the CPUs' physics really that different from the players'?
Yes. Super Mario Kart is a pretty typical example of a cheating computer. There's even a term for this - "Rubber Banding." Rubber banding is a way to balance game difficulty. The AI will always catch up to you, regardless of how far behind they are. The intent is to keep the game close without having to program a complex AI routine for driving the karts.
They also out right clip through course obstacles like Thwomps and pipes while you need a Star to smash through the same things yourself. The only thing they they can bump into that slows them down are the walls and that's if you push them hard enough into a wall.
So yes, they cheat. Blatantly, obviously, and unfairly. :) This is an issue in many games - even recent ones. In Saints Row 3, for example, the AI can drive trash trucks like they're sports cars if they so desire. They can also speed up to intercept you when you're driving the same car as they are, and you've got the throttle to the floor.