I imagine it will only be a short time before this thread gets moved to Video Games...
Strategy: I loved Sudden Strike, although it did get mixed reviews by others. It seems that the reason that I liked it, and the reason others dislike it, is that it is not the conventional RTS. There is no resource management or building units--You're simply given an army and an objective. I think it's fantastic.
Currently I'm playing Desert Rats Vs. Afrika Korps. It's a great game, except for a lot of stability issues. I'm writing a review of it shortly.
FPS: For me, it begins and ends with Battlefield 1942, and it's expansion Road to Rome. (I refuse to play the Secret Weapons expansion on principle.)
I have one of the versions of Medal of Honor as well, though it's too linear for me. It was fun, and I played through it all, but it doesn't have much replayability.
Others: I think my all time favorite WWII game is Microsoft's WWII Combat Flight Simulator. Good fun.
Silent Storm was incredibly fun until it got incredibly stupid (about halfway through the campaign).
And lastly, I still play the old Axis and Allies computer game. I get a kick out of it.