The following are some excellent Mario Kart shortcuts. Note: Reverse directions if playing on mirror tracks:
Maple Treeway Between the starting line and the first corner, veer to the right. You will see a dirt path in a gap in the fence. Drive through here to find boost pads and some boxes. This shortcut drops you out right at the warp jump point.
Mushroom Gorge This shortcut definitely requires at least one mushroom boost. From the starting line, lean left until you see a red mushroom in the distance. Aim for it and, just as you are about to go off the track, hit the boost. You should land in the middle of a red mushroom hidden below the track which will bounce you on to the next one and then bounce you back onto the boardwalk.
Wario's Goldmine During the section where you have to evade minecarts, stick to the left. Follow the last minecart. You will notice that it is lifted off the track-- aim to drive under it and you will land on a passage way with boost pads and boxes. this will let you out near the finish line.
Daisy Circuit Between the first two corners and the roundabouts you will see a flight of stairs. Best to boost up these, but driving normally works fine. This will lead to a box and a boost pad with a jump. You should land at the second roundabout.