Selfish. Greedy. These are two personality traits that go into a "me-first" player. They are in the game for themselves, either to make a lot of money or to make their stats as great as possible.
The NHL has had more than a few of these type of players don one of their team's jerseys. The NHL doesn't mind because these players are usually big money-makers for the game as well, and as long as they are, they will be accepted.
Here are the top 20 "me-first players" in NHL history.