In the original Super Mario Kart, it might not be immediately obvious, but the computer-controlled drivers follow a pretty clearly defined path around the courses. And if you can figure out where they go, you can use it to your advantage.
My favorite spot to do so is on Mario Circuit 2.
You'll notice that down toward the end of the lap (in the shot above), that there's a place where you have to jump over the track to keep going. That's where you'll strike.
Place your banana peel or green shell between the 2nd and 3rd sets of arrows, that's where the computer drivers want to take the jump. Then, the next driver that comes along will crash into your trap, lose all of their speed, and miss the jump, making them repeat a good portion of the track.
It's kind of hard to tell from the shots here, but Yoshi's fallen for it.
This is really handy if you're playing the harder difficulty levels and the battle is really close for first place is tight. Once you lay this trap, the battle for first won't even be close.