I got Dominion a couple of years ago, opened it and looked at the directions . . . and got completely overwhelmed. They look incredibly complex. Is there a cliff's notes version of the directions?
You just need to play through it once or twice. It's not complicated at all. My 8 year old can play this game. And it's a fantastic game.
I just played this one for the first time the other night. It takes one time through to really get the hang of it. It's a nice game, but it can be a little long so I wouldn't recommend it if you want to play other games in the same night.
I don't think I've ever see the game take more than 30 minutes, which is short compared to a lot of the other games in this thread.
I'd be interested in knowing what games people think are just as good but take less time - are there any 10-20 minute games of this quality out there that are good for families?
Zooloretto is short, dunno about 20 minutes though.
Race for the Galaxy is very short, probably in that range once you've played about 3-4 times. Love Letter is a very short game.
But the real winner is
7 Wonders. 18 turns long, each played simultaneously. Game averages about 45-50 minutes through the first few playthroughs and then it clicks for everyone and you can play it with a group in 25-35 minutes, no matter the size of the group.
7 Wonders is my group's favorite game to play, deservedly so. Your primary actions and strategies have long-term effects on you and your neighbors, and since it's played simultaneously, you're always engaged in the game, not just waiting for someone else to go. The expansions make it better (Cities adds one turn to each round, too). The games are never the same, especially if you change who you sit by, and randomize the wonder boards.