Anything turn based should be fine(pokemon, JRPG, civilisation). Most old style adventure games aren't time dependant, so you could get away with those(psst, get Indiana jones and the fate of atlantis or one of the Monkey Island games).
You can play almost all RTS games with one hand to some degree. Could be fun to play though a campaign on an easier difficulty.
You can play almost all RTS games with one hand to some degree. Could be fun to play though a campaign on an easier difficulty.