I'd highly recommend so called 'euro-style' board games. The classic euro-style game is Settlers of Catan, but some others I've played are 'small world', 'war of the roses', and 'Carcassone'. They're typified by fairly quick play (a couple of hours max, usually), plenty of options, a bit of random chance, and resource management.
In my opinion they are far superior to games such as monopoly, which I think is boring and too reliant on chance.

Now you've done it, going and mentioning SpaceHulk!
Don't forget, Axis and Allies, Munchkin, Settlers of Catan, Carcassone, etc. There's even digital versions of many of these.
If you want to go on boardgame crack I might suggest Blood Bowl (XBox 360 version also available).

Well I was going to suggest Warhammer 40K but its a bit much with complex rules and miniatures. On the upside you could beat everyone up with a dreadnought...

Munchkin is the best game I've ever played on a desk top. Catan is fun too, since I'm a douche bag and start the game off controlling at least one of each resource.

Or you can stop being a genocidal Space Marine and swarm the opposition with a ton of Tyranids. Ah, memories...

When I play with my usual pack of friends, it's funny how each one has his own playing stile, and sticks to it like it's life or death.
One always builds roads like crazy, one is the knight-thief resource blocker, one has this genius idea to always try to block one resource for himself (usually the most important one, like iron), and I try to position villages on as much numbers as possible (that way you get some goods each turn).
For now, no one has had a winning streak, so no stile is preferable - that's the sign of a great game. And the trading part of the game is the best one, when you need that sheep, you talk like a hostage negotiator :D

Boardgamegeek is what you are looking for, and as a fellow Czech, I can confirm most of the games in their top ten are available here, translated, and are great.
Settlers of Catan and Carcassone are excellent for board game newbies and will last for a very long time. Longer with expansions, though to be honest, Carcassone's expansions feel like a money grab more than anything else. Once you are ready for something more serious, I'd say go for Puerto Rico (probably my favourite boardgame ever), possibly Power Grid, and once that starts feeling too simple, Agricola. These titles alone will keep you occupied for months.
If you want a simpler card game for two players, Lost Cities are a safe bet, but be warned that your girlfriend will probably beat you regularly in this game. Mine does. And so do the girls and wives of many a guy, I'm still not quite sure why. A simple, dynamic card game that is guaranteed fun for 4+ people is 6. nimmt / Category 5 / 6. bere (Czech release). The packaging is ugly and unattractive, but the game is a blast.

Thanks for all the replies, guys! I'd say we'll try the Settlers of Catan or Carcassone first. I'd love to try both, it's a shame boardgames in Czech Republic are so damn expensive. Oh and Munchkin looks great too, will have to try that eventually.
Now you good sir have been extremely helpful. With the link to Boardgamegeek, I'll be actually able to find those boardgames I wish to try on my own :D Thanks. And I think I'll be getting Puerto Rico right after the first two games mentioned in this post: It does look fantastic.

One of our players controlled almost all the sheep resources and we kept making fun of the fact he is from New Zealand. ;)
How the hell do you get wood from 4 iron?

What do you mean? If you mean that if I had four cards with iron resource, I'd try to trade it with someone who has wood. If I had no port and no one to trade with, I'd trade with the bank 4:1, with a normal port it would be 3:1, and with a special iron port with a 2:1.

did he utter the infamous "got wood for sheep"?

-_- Ordered.

My work here is done.

Someone had said something about being able to crunch 4 resources for another.

Yes, you can do that at any time. 4 identical resources can be traded for another with the bank. 3 if you control the general port, 2 of a specific resource if you have the appropriate port.