How much ping do you need to play online games

Depends on game type. Ping less than 100 ms should be playable for all types of games, but for games where fast reactions are needed players with lower ping may have an advantage. On the other hand, if all players have similar high ping the play is at least even. For playing shoot-them-ups low ping is an advantage, unless the game engine evens game for high ping players. Flight simulators are not so demanding, since planes follow laws of physics and can not suddenly change speed or direction. Car driving games are somewhere in betveen. For games like chess or similar, where players may use tens of seconds or minutes to ponder the next move high pings are not an issue.