If a player is considering a call, can he show one of his down cards to entice a reaction from the bettor to see if he should call or fold?
If there are any players who will act behind you, no. It is unfair to the other players to give your opponent information that might affect them.
In a tournament, no. It is unfair to use this advantage that players acting before you didn't have.
In a cash game if you are head-up, or last to act with all other players all-in, some clubs will allow showing cards, as this is not unethical or unfair in this situation. Ask your floorman.