Personally, I find it somewhat difficult to find enjoyable games, as most of the popular games have comic-style graphics (Plants vs. Zombies, etc.) and very repetitive sounds (Angry Birds, etc.) which for me ruin the whole game.
Anyway, from the few dozen or so games I tried, the following four games are my favorite ones)
Rise of Atlantis (very atmospheric game. At the core it is a puzzle which is integrated in a journey around the ancient Mediterranean sea. This is in no way a complex game, however the visuals, music and background information through short video scenes complement the game so well that it is my most played game)
Mach Defense (tower defense at it's finest.)
European War 2 (Similar to risk, but with more options) There are various maps & more cards for bonuses. The campaign mode let's the player replay certain moments of wars, such as the invasion of Poland in WW2. Overall a very enjoyable and varied game and with more replay value then the original risk by EA)
The Settlers HD (a complete port of The Settlers 4)