Tecmo Bowl is a great old-school game where you can choose from one-player, two-player, or coach mode and try to win as quickly as possible.
The NES version could only be played by two people, while the arcade version could be played by four. There were three ways to play: as a coach, as a single player, or as a pair. In one-player mode, the player could choose a football team to play against the computer. After a win, the computer puts the player on a different team. The two-player mode and the coach mode let the player and another person play one game together, but the coaches only let the players choose the plays (which is impossible in the arcade version).
In both versions, there were only four offensive plays in the playbook. On defense, the player picks the play that he or she thinks the offense will pick. If it is chosen well, it will cause the offensive line to collapse and the receivers to be well-covered.