[dvdfvo]

You could play any kind of turn based games over planets. In the future even non-turn based games are going to be played, although indirectly.

A fun game would a real time military strategy game where the delay for both planets is artificially made the same. Then the command delay becomes part of the game, but the game still runs in real time with information updating as soon as it is available.

[Apocryphon]

People aren't going to stop playing chess or go, after all.

[hnal943]

That reminds me of Neptune's Pride, which is a game that leverages latency for dramatic effect: http://np.ironhelmet.com