We've owned Carcassonne for a quite a while, and it's one of our favorites - it's a wonder I haven't blogged about it before.
In Carcassonne you are building a city, essentially. On your turn, you draw a tile randomly, and then you add it to the existing map. Your tile may have a portion of a town, a road or a monastery. Once you lay your tile, you then can lay one worker on the tile that you just laid. Your workers collect points for you based on the jobs they are doing - farmer, knight, monk, or robber. You have a limited number of men, so you want to be wise in where you place them. Different jobs earn different values of points. Some jobs last a long time - others allow you to get your man back (so you can use him again) relatively quickly. The trick is to use your men and play your tiles in a way that will get you the most points. The game ends when there are no more tiles to be added to the board.
Carcassone is for 2-5 players, plus there are about 1.5 gazillion expansions - most of which I know nothing about. We love this game because we can teach it to people in about 10 minutes (at the most), and it can be played in about 20 minutes. We have played plenty of times with people who have little or no experience with the game who still manage to win, so it's great in that way too.