Need For Speed 3: Hot Pursuit

Shortcuts:
Aquatica:
After the first left, right, right, right turns, there is a shortcut entrance in the right wall during the next long, gradual left turn. Turn right when you exit the shortcut.
Right before the tunnel that takes you back onto the boardwalk, you can go off the road to the left, drive over the tunnel and land back on the track on the other side. It doesn't save much time, but it avoids slamming into the side of the tunnel.

Atlantica:
About halfway into a lap, after the "Electronic Arts" landmark, take the left path, then right. A shortcut entrance is immediately in the right wall. Turn right when you exit the shortcut.

Empire City:
On your left side just after the start/finish line there are light poles. Immediately before the 4th light pole there is a shortcut entrance. When you exit it, go straight: a little to your left is another shortcut entrance. Turn right when you exit that one.
Near the end of a lap, immediately after the second set of concrete pillars, there is a "fake wall" on your right side. Drive through it to drop to the lower level. This saves 2-3 seconds.

Redrock Ridge:
About halfway into a lap there is a difficult left hairpin turn. There is an alternative left turn immediately before the hairpin.

Rocky Pass:
Just past the falling-rock road sign there is a small, short cave tunnel off the road to your right. Driving through it instead of taking the sharp right turn on the road saves time.

Country Woods (backwards):
About halfway into a lap, after the 90-degree turns, there is a difficult left hairpin. A few seconds before it, make a sharp left turn with the handbrake and drop to the lower level, then press the reset button while in the air. You recover at once and skip the hairpin, saving at least 3 seconds.