It can be any Unreal game.
I'll list them here.
Unreal
Unreal : Return to Na Pali
Unreal II: The Awakening
Unreal Tournament
Unreal Tournament 2003
Unreal Tournament 2004
Unreal Tournament 3
Unreal Championship
Unreal Championship II: The Landri Conflict

I personally love all of these games. I've played all but one of them, Unreal Championship 1.

I played Unreal Tournament on the PS2 alot with my friends when it first came out but I dont think I played the other ones.

I've only played four of the series: Unreal Tournament 2003, Unreal Tournament 2004, Unreal Tournament 3, and Unreal Championship II: The Landri Conflict.

My favorite of the series is definitely Unreal Tournament 3, I still play this game rather frequently on the 360 (still trying to get the achievement for beating the game on Hard).

My second favorite would be Unreal Tournament 2004, because I played it for years on the PC (even though I only played single player), and right behind it would be Unreal Tournament 2003.

I only played Unreal Championship II: The Landri Conflict once at a local game store (where you pay to try it out) and I really didn't like it. I don't know if it was just the fact that I wasn't really sure how to play it at the time (If I remember right, it had melee weapons? I think I just kept trying to use those and never used guns). I may end up trying to find it used for cheap somewhere and give it another chance.