Not in any particular order and not counting remakes (because those are just graphical updates of older games):
Adventure games - PC:
Dreamfall: The Longest Journey
Secret Files: Puritas Cordis
Lost Horizon
Gemini Rue
Gray Matter
Adventure games - DS:
Any of the 5 Ace Attorney games (although the first Phoenix Wright and the third (Trials and Tribulations) are by far the best in the series)
Secret Files: Tunguska (discovered it on the DS, never played it on PC)
Hotel Dusk - Room 215
Last Window: The Secret of Cape West
The first 3 Professor Layton games
Shooters:
Call of Duty 2 (is that still within the last 5 years? If not, no shooters - been disappointed by the genre ever since CoD2, the last great shooter)
RPGs:
Mass Effect 1 and 2 (can't wait for the third and final installment)
Dragon Age 1 and 2
Sports:
Tiger Woods PGA Tour 10 (I have the WII-version)
FIFA 12 (although the PC version is buggy as hell and crashes often, it's still the best FIFA game since '99)
Football Manager 2007/2009/2010 (didn't play the other ones, but looking forward to FM12 which gets its release today)
Tennis Elbow 2011 (indie fave!)
Strategy:
Civilization IV (and if that's not from 2006 or newer, replace it with Civ V
)
Other:
Chessmaster XI - Grandmaster Edition
Ports of Call (indie fave!)
And if you force me to make a top 5 out of these, then they'll be:
1. Mass Effect 2 (made my all time favourite top 5)
2. Phoenix Wright - Ace Attorney
3. Phoenix Wright - Ace Attorney: Trials and Tribulations
4. Tiger Woods PGA Tour 10
5. Lost Horizon (underrated, imo)