I adore deck-building games. The combination of skill and luck makes for plenty of puzzling and adrenaline.
If you're not familiar with this kind of game, here's the basic idea: everyone starts with a few cards. You shuffle this deck and draw a hand (often five). You use those cards to buy other cards (or take other actions), then discard the whole lot. When you run out of cards, shuffle everything that's discarded, and go again. As the name indicates, you "build" the deck that you use to play the game -- trying to secure strong cards and thin out weak ones while keeping a balanced deck that will yield, on average, good hands.
Here's some great deck-building games. I've played about twice as many deck-building games as this, but I figure there's not a lot of point in drawing attention to games I don't jump at the chance to play.
I actually had a hard time picking up the rules because no one bothered to explain them to me -- they were too eager to play and I had to learn by watching. But, being a new player isn't a huge disadvantage. The cards available to buy change every game, so there's not one master strategy to victory. The downsides? The cards have a decent bit of text on them, which means pausing for people to read and re-read cards. Also, there's lots of shuffling.
Like Dominion, the chips change every game, keeping things fresh. Everyone also gets a character with their own special chips. But there are no victory points. It's a last-man-standing, get-your-opponents-to-crash kind of game. It also plays super-fast. Multiple games are a must. Added bonus: you draw more chips the closer you are to losing, so it's quite possible to catch up from the brink of despair.
ETA: The 3rd edition has made some major changes to the game, changes that I think sadly steers the game into randomness and kingmakers and away from a kind of balanced chaos. I'm very happy I have an earlier edition.
At the end of the game, the player with the fewest wound cards win. Part of the game is thus also trying to look like you're not winning so your opponents attack someone else. I know a few people who find this frustrating, but the back-stabbing fits the game.
The version I played did have a runaway leader problem, but I've been told the rules have been adjusted in the newest edition. The changes made a lot of sense and would smooth out the problem. Even with the problem, I still enjoyed the game. It was short enough that if I was doomed to loose, I could wait ten minutes for the game to end, then jump back in again.
The only downside is the set cards. The card available never change, meaning you only have to adjust your play to what's in your hand. Often, I don't like expansions (they tend to add fiddly-bits without increasing my enjoyment of the game), but I hope Eminent Domain comes out with one to increase replay value.
Any favorites that I left out?