What sports can you still play with a broken arm?

Depends. Sorry to say it again but it all depends upon what he injury is. A non displaced fracture is difernet from a fracture that requires reduction , or internal fixation ( surgery) age is a factor not only fo rthe degree of injury but for who one is competing against. For example is a 5 year soccer star or a 21 year old blue liner!
Until Healed-- Until healed completely, probably chess.

Related Questions

Is it possible to play sports after recovering from broken arm? If not, why?

If healed yes. As long as the fracture has healed and there is no residual deformity that limits function resumption of sport is usually possible. Read more...