As an upgrade from my last Fav...Pong (most of you will have no clue)
I'd say Battle Field 2, battle front 2 and Tom clancy's Rainbow six: Raven Shield.
For FPS.
They all have strong online play, with ok single player games. They all play best when you work with a group and have strong squad cooperation. (but still fun when out alone)
For Strat games, any of the Civilizations series, Age of empires (one or two), Rise of Nations.
These three titles are the best of the Strat series (and some of the longest lived), the indeepth game play that is allowed, the replayablity and ability to be played for a long time with little to no boredom.... Makes them great games on my list.
A little foot note, I love Total Anhilation...but it's lack of updating, and few options to play online makes it in my oldy but goody catagory. I'm still very willing to play it in a lan setting (at the drop of a hat!!)
CrazyBillyBob