This would be excellent for improving the social side of the game.
I'd love to have a game of darts in Quarks.
I'm sure alot of people have seen those simple browser based darts games.
Should be easy to implement.
That's pretty much what I had in mind for mini games. They don't have to be super fancy or even be in 3D, they could be fun little divisions within a much bigger game sorta like how Fable2 does things with it's minigames/jobs or gambling in Mass Effect. A plus would be if they were multiplayer like you sit down for a game of chess and it pairs you up with someone else playing chess even if they are across the galaxy. This would also be interesting if/when we get to buy "funiture" for our quarters/rec rooms/captains chamber. If anything mini-games would give planets like Risa more personality (like only certain planets offer certain types of diversion).