I'm pretty sure they are legal, I think the main reason why people avoid using a clutch in their drivetrain is because they don't want any slipping before the wheels contact the ground.
The most common type of shifting (from what I've seen) is the dog-shiftuing method, like you said. There's mesh shifting, where you basically move the gears instead of a dog. Then there's more complex ones like a continuously variable transmission, or a CCT. Last one I can think of is where the robot actually switches around it's drive wheels. 980 did this in 2003, it was really neat to watch them shift,
here's a picture, it ain't that great, but you can see that they have an extra pair of wheels; larger ones for higher speed.
Edit: Just remembered, 222's ball shifting method is another one. It's hot stuff...