Oh, I just found an English version, unpunched version of Vinci for sale at BoardGameGeeks!! Score, Merry Christmas to me!
One of my favourites was Globetrotters. I had it as a kid, and then a few years ago I found it in a secondhand shop. My wife is generally a good sport when playing board games, except when she lost at this one. Neither one of us know why, exactly.
I really like the Battlestar Galactica board game…they managed to take an awesome show and make an awesome game out of it. Cosmic Encounter is always fun, occasionally very strategic. Dominion is growing on me in a big way, and I think I’ll grab the expansions soon. I just got Chaos in the Old World, which looks like 8 kinds of awesome but I haven’t played it yet.
Next purchase: Pandemic. Cooperative gameplay fighting diseases around the world? Yes, please.
Pandemic is lots of fun, but tough. My group’s success rate at saving the world is not good.
Pandemic is indeed lots of fun, and my family plays it maybe once a month. It should be noted that it’s a cooperative game, though, and in that sense some might deem it more puzzle than game. ETA: oops, someone did mention that. So much for my mad thread-reading skillz.
EXACTLY why you shouldn’t pick it up! 
Lots of great suggestions here but you’re missing my favourite. Mancala is simple enough to teach a four-year old and complex enough to keep adults interested.
I just heard about Mancala recently. We played Oware growing up and it did indeed keep kids and adults interested. Same with Parcheesi.
When I’m not busy with Mornington Crescent, I like:
Case Blue. It’s a regimental level simulation of the 1942 campaign in Southern Russia/The Caucasus region using The Gamers OCS system. I’m bound and determined to master the Soviet Steamroller to surround Stalingrad.
I also like Monty’s Gamble"Market-Garden. An area move game about A Bridge Too Far airdrop on Arnhem, The Netherlands.
For non-wargaming fare, I really enjoy Le Havre and Small World, mentioned above.
We have been enjoying a new game called Marrakesh, in which the player is a rug merchant trying to corner the market at a bazaar.
Ok - I love board games, but I have 2 current games that are card games and I love them!!
Dutch Blitz - it’s rapid fire and heart-pounding when you get 4 people playing. Who knew the Amish could have so much fun? I played this game in college, and just bought a deck recently and introduced it to some of my friends. We had people lining up to play high-man out (where the winner of the round sits out and lets someone else cycle in.)
Fluxx - the rules start off simple: draw one, play one. And then all havoc continues as players get to change the rules, how to win, who has what cards, etc. You could have the winning card in your hand - only to have the player before you totally change the entire game!
Once you get Fluxx down, then you upgrade to Zombie Fluxx, **Monty Python Fluxx **or some of the other expansions.
It’s always a real crowd pleaser for us and our group of friends.
Since my username gives away my favorite board game, I’ll skip that obvious one- even though it’s the most famous and most played game in the history of mankind. 
As a kid, I loved Key to the Kingdom. You’re an adventurer that travels around the board defeating obstacles with rolls of the die. You have to slay dragons and navigate rope bridges over pits of doom and the like. Your quest- collect treasure and The Key, so you can rule over whatever-the-place-is.
As an adult, I like Tie One On. There are 3-6 players. Let’s say there are 4. For the first round, player 1 works with 2. One draws a card and tries to get 2 to guess the word on the card so he can move onto the next word on the card. Get as many as you can in 45 seconds. The twist is that on player 1’s next turn, he’ll have to work with player 3, then player 4 after that. So it’s a team game, but your team always changes! Great fun for the whole family!
Buyer beware. This was fun when I was 10 but now it’s just annoying. The easy puzzles are ones you’ve heard a million times (“The killer used an ice cube that melted later on!”) and the hard ones are impossibly difficult (“A time travelling vampire with a penchant for coca-cola killed the goat with a razor blade that was half-off at Macy’s”). But if you’re into either of those sorts of things, have at it. It’s a good game for a road trip, as you don’t need to see a board, roll dice, or hold cards.
This is actually a well-studied and seriously played game. There are documented openings, such as these that you need to know to truly be good. I hear there are even tournaments held in various cities at various times.
Most computer versions will have different difficulty settings, and part of the difficulty seems to be which openings the computer knows at that level. Another part is how many moves ahead the computer is allowed to look. However, no matter how good a computer is, a human on the other side of the game board is better. A computer won’t overlook a move, while a human might, and if your play depends on your opponent falling into a particular trap, then a human might not see the trap…or might recognize it. I spent a lot of time on my old TI99/4A with a Reversi cartridge, and it was pretty good. However, I got into the habit of counting on my opponent to make certain moves. Once I was able to go online and play against people who might or might not know me and my habits, I had to learn more about the game.
Sometimes I wonder how different the game would be if it had an uneven number of squares per side.
http://en.wikipedia.org/wiki/Diplomacy_game
An old game, but an absolute classic. So simple but so rich with possibility.
Getting seven players face to face can be difficult, so I usually play on this site:http://www.playdiplomacy.com/index.php
I love Kill Doctor Lucky. It’s sort of a reversed version of Clue (or, a prequel to Clue)…the players chase Doctor Lucky around, trying to get him alone so that they can kill him, out of sight of everyone else.
Another vote for Settlers of Catan here. We’ve enjoyed it, and its variations, for many years.
We used to play Empire Builder quite a bit, but it’s a pretty lengthy game…plan on it taking 3 hours.
When I was in college, we loved Cosmic Encounter (the original Eon Games version). I’ve heard that the versions made after it left Eon weren’t as good, though I’m tempted to pick up the current version (from Fantasy Flight Games).
The End of the Triumvirate is my current favorite board game. Simple yet elegant and by far the best 3 player game I’ve ever tried.
History of the World is also a game I can’t stop recommending, like Risk but played out in 7 historical epochs. The goal is to acquire more points by taking over important areas while they were historically valuable. Your Egyptians got wiped out to the man? Thats alright, you’ll have your revenge when the next Epoch comes around.
I’m a huge proponent of fun learning and if I taught a junior high history class I’d give bonus points for any kid who plays this after school.
Must…resist…temptation…
Actually, I wonder if there are enough SDMB players to start a game.:dubious:
We’ve had a few here, actually. Do a search for “Diplomacy” in this forum and you should find one pretty quickly. 
Axis and Allies.
Critical to a successful game of Axis and Allies is having five players and the right equipment:
- An Axis and Allies set,
- The “World at War” expansion,
- $60 and the number of a good pizza place,
- A lot of Tostitos and salsa,
- Two cases of beer, and
- A place you can play for eighteen consecutive hours without pissing off anyone’s wife or girlfriend.
In college my favorite board game was Axis and Allies. We’d play literally for days, with no set alliances in the game…each player could decide on who, if anyone, they would ally with. Countries were given out by the draw.
-XT