Being me, I like to play (side by side/across the desk from one another) Counter-Strike or Call of Duty type games.
If you like RTS's and haven't played many of the older ones, go for games such as Age of Mythology, or if you're experimental or REALLY like the older RTS's, go for Total Annihilation: Kingdoms. Or the original for that matter.
Those are just what we've played recently.