I didn't have to give this too much thought to know what my favorite machanic is. Drafting.
My love of drafting goes all the way back to Magic the Gathering. There is something unique about being able to build your hand based on quick decisions and trying to figure out what other people will take.
#7 Wonders is the game that really solidified this for me (and it is my favorite game. It actually has something that is better than just drafting, and that is simletaneous drafting. Beyond building your hand (or tableau), all players are drafting at the same time. The great result of this is that the game is always moving, with virtually no downtime. You are always looking at your hand, picking and playing a card.
The ability to draft before a game to set up a strategy is fun as well. #7 Wonders: Leaders, #Seasons, #Monster City Planners, and even #Agricola do this. It can turn a good game, into a great game (at the cost of a little time).
What is your favorite drafting game? Are there games where drafting doesn't work for you?