Players can only play one BANG! card per turn. This applies only to BANG! cards, not to other cards with the BANG! symbol (like the Gatling).
Players can only have one copy of any one card in play. A card is a copy of another if they have the same name. Cards in front of the player are defined to be "in play" until they are removed. There is no limit on the cards a player can have in front of him provided that the cards do not share the same name.
Players can only have one weapon card in play. When a player plays a new weapon, he first discards the one he has in play.