Unlike Onder, though, I'm going to give two huge thumbs down to Terra Mystica. The game has far too much on-board complexity, with scads of game pieces to keep track of and multiple boards to monitor, giving rise to analysis paralysis for all but the most seasoned of board gamers. If your playgroup consists mostly of Magic players, who are used to analyzing complex board states and filtering out the useful information from the irrelevant, then perhaps give it a try. But if your group consists mainly of casual board gamers, I'd stay far, far away. I don't feel that the level of fun this game offers scales in proportion to the number of fiddly bits in the box (and I say this as someone who crushed the one game of Terra Mystica I played, taking 20 second turns while everyone else muddled about for five to ten minutes at a time).
Actually, in my experience it's the other way around. I've had great fun with casual gamers, and I've only heard negative things about the game from hardcore gamers. Casual gamers are more likely to just have fun, enjoy the flavor of the game, and do stuff. It doesn't really matter what you are focusing on, you will get points anyway. The analysis paralysis is not a problem for the casual gamers, it's a problem for the maximizers, i.e. the hardcore gamers who want to win and thus want to calculate their every move. It is also a game with very little luck, so there is a lot you
can calculate, and your possible moves and thus your calculations change all the time. With slow maximizers the pace can become painfully slow. As I said though, I never had that problem with my casual gaming group. They (and I) are just having a lot of fun flying around on brooms and carpets, digging tunnels, and swimming up and down the river
For quick games I'm a fan of
King Up! and
Boomtown. King Up! especially is very beginner friendly, and full of bluffing and deduction. The game gets especially hilarious when your players have a gambling streak and start counting on others to veto an heir to conserve their own number of veto's. Boom! Suddenly someone is crowned king to the dismay of everyone but the single honest player who wasn't bluffing after all when he pushed the heir up to the throne room
Boomtown is a nice western-themed card game where everyone is building mines to earn money, trying to become mayor of multiple towns to earn taxes, and hoping someone doesn't throw a stick of dynamite into their saloon. Plus it has nice chips that fly back and forth over the table.
Oh, I almost forgot
Dixit. Also very casual friendly. The game consists of nothing but a stack of cards with full art, often a little weird. One player is the storyteller (everybody takes turns taking on this role) places a card in his hand face down on the table, comes up with a short phrase or a word describing that card, and then all other players get to add face down to the table a card from their hand that best matches that description. The storyteller shuffles the cards, deals them face up, and all the other players start guessing which card was chosen by the storyteller. Every other player then gets one point for each vote for the card he put on the table, as well as points if they chose the correct card. The trick is that, as the storyteller, you get a set amount of points, unless either everyone or noone guesses your card correctly, then you get no points at all. So you want to be cryptic, but not too cryptic* **.
* The game stops being fun, by the way, once a pair of players start to hint at private things that only they can know, like: "Jimmy", when Jimmy was the dog of one of the pair's parents when both players were still young. Other players can't be expected to be able to know that stuff, so it's a good way to score points, but a miserable and thoroughly unfun tactic to play against. Don't be a dick and chose fun descriptions people actually have a chance at figuring out.
** I always manage to think three steps too far ahead, so my descriptions are usually so cryptic not even an all-knowing entity could guess what the heck I was thinking. I'm not very good at Dixit, but I
am having fun