Even though I picked some modern games, my all time favourites from "modern" computer gaming would have to be the original Deus Ex and the original Far Cry. Deus Ex really set the standard for the modern games and was really ahead of its time. The original Far Cry (a much better game and story than its descendants) was just so bloody enjoyable and had such a great story that I have found few games that can compare to it.
I still consider EQ one of the best games I ever played. There are not many games that I can still recall the places I visited as if they were real, lol. Kaladim still feels like home!
Honestly, I still miss the game. No other mmorpg has ever come close. At least for me.
I guess it depends what you mean by modern era.
If we are talking about games released since PS3 was released...that's still too many games to list just one.
I will list a few of my favorite games released over the last decade or so.
Rainbow Six Vegas 1. (PC)
Split Second Velocity. (all)
Two Worlds 1 (PC)
PGR 3 and 4 (Xbox 360)
Ridge Racer Unbounded (PS3/PC)
Horizon (Space 4X PC)