Oh, where to start...
I've been a member of a SU dedicated to boardgames for years. We have literally hundreds of boardgames, ranging from shiny new ones ot forgotten gems like Advanced Squad Leader, The Peleponesian War, a mint condition first run of Titan etc.
We used to be big on Arkham Horror and Battlestar galactica, but both games suffer from the fact that gameplay is defined by event cards. Once you've played it enough times, the game becomes predictable. Until then though, they're solid fun.
Games we frequently play so they should pass as the good uns:
Android - This one has a LOT of rules to parse, so teaching new players is a pain. It's similar in many way to Arkham Horror/Battlestar Galactica in that the players move around the board and try to build up some sort ofpoints with characters that have unique abilities. The setting is very Blade Runner, and there are multiple ways of getting the Victory Points required to win.
Small World Berserk Hobbits! Mounted Amazons! Flying Warlocks! Merchant Orcs! The spiritual successor to good ol' Vinci is great fun. Games are quick (1-2 hours to complete compared to most of the games we play in PFD taking 4-5), and the endless combination of [Trait][Race] makes every game slightly different. Gameplay is complex enough that the grognards in PFD are willing to play it, yet simple enough that I could explain them to my parents and have them asking me where they could buy the game. Highly reccomended.
Twilight Imperium - I'd definately reccomend getting the expansion for this, as the rule changes makes it more balanced. This is an all-nighter. 4x strategy in space. Huge amounts of fun. I haven't tried Shards of the Throne yet, but I'm giddy with anticipation.
Dominion and its various expansions. Another game that can be played in about an hour. Every game, a card bank of 10 different types of cards is built from the library, determining what actions and rules are in effect this game. Building up combos, optimizing your deck and cursing the luck of the draw is all good fun. It's like the interesting parts of Magic: The gathering (building your deck) without spending a billion potato on booster packs.
Shogun another personal favourite of mine. An unique but quick method of resolving battles, and mechanics rewarding aggressive players makes this a nice, fast-paced game. The order in which actions occur changes every turn, meaning you might end up having attacks happen before you can gather rice from that one province that may mean the difference between a quiet winter and starvation and peasant revolts. Good stuff.
A game of thrones - Mostly for ASoIaF fags. The game suffers from the fact that many factions must make a few exact moves in the first couple of rounds or another player will get an easy win. The expansions fix this somewhat. If you're a gargantuan ASoIaF fag, you'll like this.
Settlers of Catan - No board game list is complete without a honorary mention of Catan. Best played without expansions in my opinion. This is another fairly quick to play game involving resource management and inter-player diplomacy.
Civilization Ah, CiV. This game has actually shown itself as being surprisingly balanced. Every game I've played so far, there's always been at least one player who was one turn short of winning instead of whoever did, and we can usually point out the decision that cost him the game a few turns back. I love the tech pyramid, and the fact that there are different ways to go about winning the game (Tech victory, economic victory, military victory, cultural victory) makes for interesting scenarios.
Those are the newer games we play a lot. I've avoided listing th eolder, more obscure games as those can be nearly impossible to track down today. (that said, I could totally go for a solitare round of Pelephonecian WAr right now...)
If you're looking for inspiration on what games to go for, look no further than
http://www.boardgamegeek.com
It's a brilliant site with user ratings and reviews - many of which are quite well-written, giving you a good idea of what to expect before spending your potato on shiny sheets of cardboard.
