GCN Dry Dry Desert - Dry Dry Desert is filled with many shortcuts. Just about any area can be bypassed by using a Mushroom to cut through the sand. You can cut any of the turns in the first section of the track. As soon as you pass the finish line, turn to the right and use Triple Mushrooms to cut through two rocks and the large area of sand.
SNES Donut Plains 3 - Here, you can enter the second Underwater section and stay to the left. Watch for the tire tracks and exit here! Also, just before the final turn is a row of blocks with a small section missing. Use a Mushroom through this hole to cur through one of the turns!
N64 Royal Raceway - Here comes that baseball bat again. After you turn around the corner of the wall, use a Mushroom to reach the ramp on your left. After you pass the castle, use Triple Mushrooms or a Star to cut through the entire section of turns up ahead.
3DS DK Jungle - Use a Mushroom to ride up the fallen pillar just before you leave the jungle to get to the Golden Temple. You can glide over the next section from here. Unlike the 3DS version of the track, the final split in the path just before the finish line has been changed. In order to use the shorter route, you'll have to perform a sharp turn to make it over the gap!