#7 No Thanks
Plays with 3-5 players. No Thanks takes around 15 minutes to play. It's all about knowing when to pass, and when to take cards. It's quick to explain, really simple choices, and doesn't require full attention from all players at all times.
#6 For Sale
Plays with 3-6 players. A quick auction game. Players bid on houses, then use the houses to earn money. It's a fast auction game, good for a few laughs with the various artwork on the houses, and good for gamers and newbies alike.
Plays with 2-8 players. A game of last man standing. Players play tiles to move their marker on the board. If you run off the board or into another player, you're out. Really simple to learn and do well in from your first play.
Depending on the version you have, plays 3-6 or 3-12 players. Dixit is a storytelling game with quick play and amazing artwork. When you're the storyteller, you give a clue about your card, then put it in the center. All other players then put a card in. All cards are revealed and players try to pick which card belongs to the storyteller. It's a great game for kids of all ages, especially ones with vivid imaginations, but adults will get a kick out of it too.
#3 Wits and Wagers Party
Plays with 4+ players. If you have a large group, break into teams. Wits and Wagers is a trivia game where you don't need to know the answers, just have a ballpark idea. The questions are things that most people won't know, but might have a reasonable guess about. 7 rounds keeps the game short but interesting, and the questions may spark some conversation.
#2 Ticket to Ride
Plays with 3-5 players. Ticket is the most complicated game on the list, but that's not a bad thing. It's probably not great for little kids, but for the teenager and up, the game makes sense. There's only 3 things you can do on your turn: draw cards, play cards, get more tickets. You really only have to decide between the first two most turns. The game takes around an hour, but it's a great game to introduce the family into the world of boardgames.
#1 Incan Gold
Plays 3-8 players. Incan Gold is a push your luck game. With each card, you must decide if you want to take what you have and run, or risk it and try to find more treasure. The game plays for 5 rounds, so even if you don't do well in a round or two, you still have a chance. Incan Gold takes a play to see it work, but most people say "let's play again" after they learn. It's a great game for a larger group, and a lot of collective emotion as cards come out.