UltraCorps
Web-browser, turn-based, strategy game. Used to be run on the old MS zone stuff but its being revived. Right now its free and still in testing but its a pretty solid game that isn't overly complicated.
You can play a solo game and work through the walkthrough (click help). The solo game just puts you in a simple 10-15 system galaxy with nothing but neutral systems (think barbs from Civ). Lets you get used to using the interface and build orders...
Its also very schedule friendly -- the host of the game can set the turns (called "ticks") to go hourly/daily/weekly or to tick when everyone has submitted their turn.
My roommate and I are trying to get a game going so if anyone wants to play hit me up on AIM (eidal12345) or PM me for an invite.