Carcassone is quite easy to play, and allows for both cooperation and competition between players. Scoring is a bit complicated at first, but after a couple games, you'll have it down pat. The real fun of this game is in placing the tiles and building a countryside, and the gameplay itself is so simple that I can play this game with my 5-year-old cousins (minus the scoring, of course). Additionally, there's a metric buttload of expansions for this game available, each of which adds new tiles and new rules elements. Personally, I recommend this game more often than I do Settlers of Catan, (which I find to be too easy to become unfair and unfun when players vary widely in skill-level).
As for Munchkin (the card game, not the boardgame or RPG spinoffs, which I've never played) is a fun game, especially if you're familiar with the tropes of D&D -- Munchkin is a game that satirizes various genres, but especially fantasy gaming. There's also tons of different thematic "versions" and expansions of this game, all of which are compatible with the rest. That said, the rules are dirt-simple to learn and use, and in four years of playing it I've never came across a major "rules dispute". The downside to Munchkin is that there's a strong air of informality to the rules of the game, which actively encourages cheating, in the spirit of humourous gaming. This game is a lot of fun to play with your gaming friends, although a lot of the humour is lost on non-gamers, and overly serious and over-competitive folks might not enjoy it. Overall, Munchkin is a great game, as long as your players aren't wound too tight.