Picard: equestrian, marathon or fencing
Worf: any martial arts will do.
Beverly and Deanna: gymnastics. Failing that (if it isn't an olympic sport): turning.
Not sure if Geordi would qualify for the Paralympics, perhaps without his visor. With his visor, I really wouldn't know which sports would suit him more than any other.
Riker: any sports that will make him look good for the ladies
Data: probably disqualified because of his inhuman strength and speed, both mentally and physically. If not, he would probably be extremely succesful in any sport, not sure which one he'd choose. Perhaps swimming, since 'he has been designed as a flotation device', which would give him even more benefit.
Q would participate in boxing, only to get the shit kicked out of him and then complain to everyone in sight that 'Picard never hit him'.
Oh, and for ball sports, Odo would probably make an goalkeeper that can't be beaten. He simply morphs into a rectangle that fills the entire goal post.