I play a lot of boardgames. Possibly too many (if that's a concept that even makes sense.) If you're not sure whether the hobby is for you, then here are a few suggestions:
The best way to get into boardgaming is to have a friend with a tried-and-true boardgame group who can invite you along; that's generally the best way to ensure a good experience. However, since not all of us are lucky enough to know "that boardgame friend", a good secondary option is to call up your local boardgame shops and ask if they have a drop-in boardgame night. Bringing a friend along can be a good way to reduce the alienation factor of playing with a group of strangers. Many stores have a shelf of open games you can try out for free, and are often full of friendly gamers who are more than happy to teach you how to play. If you get an uncomfortable "we don't care much for
strangers 'round these parts" vibe, though, walk out the door and never return to that shop.
As far as what games to play, can you tell me a little more about what you're looking for? In particular, are you more interested in playing games with particular themes (E.g. zombies, fantasy, whatever) or are you more interested in how the game is designed, with the theme being secondary?
Here are some popular beginners' games:
Simple games: Bang!, Bohnanza, Saboteur, King of Tokyo
These are analogous to "causal" computer games like Plants vs. Zombies - they're a light and fluffy way to pass a bit of time, and have a little bit of strategy without requiring too much concentration. Fluxx and Munchkin would also fit in this category, but personally I find those to be
too simple.
Medium-light games: Settlers of Catan, Blue Moon City, Seven Wonders
These are good intro-level games - they start to show you the possibilities of more complex strategies, without getting overwhelming.
Medium games: Peurto Rico, Cosmic Encounter, Dominion (or its zombie equivalent, "Resident Evil Deck-Building Game"), Neuroshima Hex, Smallworld
This is where the magic starts for me. These games can still be taught and learned in a single sitting, but it takes a little more effort to understand the strategy and start playing "well". I'd recommend having a few gaming sessions under your belt before trying any of these, but if you find yourself intrigued by the more strategic aspects of the medium-light games, you may want to try some of these out.
keeveek: Btw what about Talisman? It looks awesome and it has quite few big expansions (and few little ones). It looks like this game fits my preference in setting perfectly. But it's quite expensive, so I would like to hear your opinions
http://boardgamegeek.com/boardgame/27627/talisman-fourth-edition My experience with Talisman is that it plays a bit like monopoly with elves - i.e. a lot of dice-rolling and then just seeing what happens, without much thinking involved. If you're really into the fantasy theme, though, it might be your thing.
Re: your question about FTL, the boardgame that plays closest to that is Battlestations. Battlestations is an awesome, awesome game, but it's also pretty complex (it's almost a tabletop RPG), so I wouldn't recommend it as an introductory game unless you have someone running it who really knows what they're doing.