Board game disucsions
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I've been trying to arrange times for my family to get together to play board games. Given the increased popularity of late and comeback of boardgames, has anybody out there discovered some new ones that are really fun and easy to learn? Usually this sort of thing is after a dinner so people generally can't handle complex board games on a full stomach...so no "Third Reich" or "Supremacy" with last 50 add-on packs. 
Yes. (discovered new games)
I've pretty much continued to play and work on board games since then. So has Jason. Currently I am also in three distinct 'board gaming groups' (one at work, one w/ family, and one with friends of friends).
I can recommend all sorts of stuff, but I think instead maybe I should first give you a clue on fishing instead of a few fish: http://boardgamegeek.com/
Now some fish. If you had asked 5 years ago or so, the canonical gateway game was still pretty much Settlers of Catan. I have always found that game frustrating due to the luck, but for after-dinner-family gaming, the luck is usually an upside. So that is still a good one. Played correctly as the base game, it is pretty short and tight.
Another one I have to bring up, just because it is so easy to pick up, plays so fast even with 5 or 6 players, has the illusion of depth, and admittedly has some immersion, is 7 Wonders. Personally, I only like the game as a 2 player game, but the fun everyone else has is hard to deny.
THE co-op game, and probably one of the best recommendations, especially when there are possibly some people in the game who are not as "into" board games as some others, is Pandemic. In fact, from what you describe as you scenario, I'd call Pandemic possibly your best gateway choice.
My favorite civ-lite wargame-lite, that is extremely simple, but actually has really good balance and gameplay depth is Antike. However, it is out of print, and can be a bit sterile for some people not inclined to play civ/wargames. Smallworld is still in print, is also very easy to learn, and also has a lot more gameplay than the rules initially imply. So Smallworld is my wargamey recommendation. Smallworld also has probably the tightest best set of rules I've ever seen. Smallworld is also shorter than Antike, which is probably good for food laden people.
Finally, what I'd call the best state-of-the-art example of a "Eurogame", and includes a "family" simplified ruleset, is Agricola. Eurogames are fun, but not my personal sweet spot, but when a Euro is to be the choice for a session, Agricola is about as good as it gets. For your scenario, this would be my non-war competitive (non-coop) game recommendation.
I think AJ intentionally left out a couple.
Carcasonne is very popular. There are a lot of add-ons and alternate forms, but the base game is good until you start looking for more twists. You can usually buy the base with the two most common extensions included, probably a good idea.
Munchkin is a surprisingly easy game to get people to play, but any notion of strategy is just an illusion. Instead of people tiring of the game itself after many plays, they get increasing frustrated with the notion that they can win by skill. It is really just a playful jest of RPG games based on a roller coaster series of random draws. Like Small World, the artistic take on the pictures really helps a lot.
Settlers has a recent rail version, which seems to level out some of the randomness issues and add some new twists. And it also has literal settlers in it.
But for actual opinions, look for aweber and baboon on Board Game Geek.
Like I said, I could say a lot about a lot of games. I first pointed him to BGG, then just offered my best-of-class for-his-group opinions.
Carcassone is an oversight, as I suppose it is probably the best-of-class for-his-group for tiling games. However, tiling games in general I would not recommend as the very first gateway or entry point, as they all seem to have niggly scoring procedure, Carcassone included. Carcassone is a good enough second game, once you have your group bought into non-Monopoly.
Munchkin I think is nowhere near something I'd recommend. Sure some people like it alot, but some people only moderately like the base game and think the epic version is absolutely busted. For mostly-cards-only, it is hard to beat Hearts as the best-of-class, but if you are looking for a broader reach 'modern' type of card game I already cited 7 Wonders. There is also the hugely popular Dominion, which a a bit longer to play, and certainly deeper than 7 Wonders. Still Dominion is a little too close to straight CCG for my taste, and I'd prefer any one of the quad of these closely related games: San Juan, Race for the Galaxy, Glory To Rome, and Innovation (although I have not played Innovation, just read the rules). Of those four, based on my plays, Glory To Rome is the most interesting and intense, Race for the Galaxy is the least confrontational (less interactive, which can be a plus for some casual groups), and Innovation looks rather cool for 2 players but reportedly falls short of Glory with more players. San Juan was the first, and sort of lays the foundation the other three ran with. However, having said that, Dominion is more 'casual' player accessible than these other ones, especially Glory. If you have any Magic or other CCG veterans, you'll hit big with Dominion.
The rails Settlers is far too long as a first game for a group. Yes, it does fix some things about base Settlers, but it is not so much any sort of best-of-class, but rather something seasoned Settlers players would appreciate. Does rails Settlers have a 'short' version in the rules? If so, that might bump it up to first-game viable. Note I would not have cited Agricola if it were not for it having 'family' rules for a shorter simpler entry point. Age of Steam (and family) is a better 'rails' game by far, but far too intense as a first game.
edit: with respect to cards games, I have to also call out Tichu. It is classic, still hugely popular, and very well respect among hardcore gamers. But guess what...I've never played it. It is a glaring hole for me.
Also, I guess I should add Cosmic Encounter. You have already played it, but that was an cheesy edition and you played with a group of kids (us) who did not really play it as intended. It is designed as bash-the-leader, embracing it as opposed to trying to mitigate it. The current edition in print is suppossed to be exceptional, with more races.