I've been hosting a board game night once a week at my place for a little over a year now I guess, I have around 40 board games at the moment, and probably add another 6-12 new ones per year, depending on the quality of releases and the interests of my group as we gain and lose members.
Some weeks I have a small group of 3 or 4 of us, and other weeks I've had upwards of 10 people show up for the fun.
Some of the favorites amongst my core group of players would probably include:
Bohnanza (The Bean Game): This is probably #1 for me and my group. It's a super simple card game that can be played with 2 - 7 people. You play the role of a Bean Farmer, and the goal of the game is to farm and harvest beans in order to earn a profit off of them. The player who earns the most money from their farm wins the game, but you have limited room as to how many different varieties of beans you can plant, and must trade and barter with the other players at the table to get the proper variety of beans that you're looking for. (There are several expansions for this game, but I have yet to find one that I enjoy adding into the base game, I think it's simplicity mixed with my core groups very vocal and entertaining antics while bartering is what makes this game a hit week after week).
Guillotine: Another very simple card game, can be taught to new players in minutes and the whole game itself generally only lasts 15 minutes or so, so nice quick game to break up the bigger and more time consuming sessions that some other games offer. Each player takes on the role of a King (or Queen) who is killing off different citizens of the populace, the citizens to be killed are lined up at the beginning of each day (3 days in a full game), and are to be killed in the order of the line.. but you have a hand full of cards which you can use to alter the line up in a way that suits your needs, as each different citizen is worth X number of points if you are the King or Queen who receives their head from the Guillotine.
7 Wonders: It's been mentioned already in this thread. I can't recommend this game enough, relatively easy to learn, great replayability, great player interaction, always a popular choice with my groups. Also I have 2 or 3 expansions for it all of which integrate quite flawlessly, only adding more depth to the game without a myriad of new rules or confusion.
Agricola: Not a game for everyone, I have a hard time selling this one with quite a few people, but I also find the people who do like it, love it. I'm a big fan of the game, but it can be quite frustrating, I also find that it ends too quickly personally, but that's part of the challenge.
Dominion (and all 7 or so of it's expansions): Great series of games, all the expansions are interchangeable with the each other. Mix and matching sets of cards between the probably near 200 amongst all the expansions into different sets of 10 to create a different game each time. Definitely one of the best Deck building games out there. Easy to teach and pick up for new players as well.
King of Tokyo: Great casual game, very easy to learn, great player interaction, great art style, great theme, nothing but praise for this game!
Last Will: A fairly new game as far as board games go, one of my most recent purchases. This game has a great theme, well balanced, great art style, and more great player interaction. If you haven't heard of it or tried it, you owe it to yourself to do a little research and check out some reviews or game play videos on it, definitely worth your time.
Pandemic: One of the few Co-op games out there where the players work together as a team in order to defeat the game. This game is amazingly well balanced, has a great difficulty level (with expansions and playing their 'hard mode' this game is nearly impossible to beat!), great theme, and tons of awesome player interaction. Can be frustrating to get beat down by a board game as a group of avid boardgamers, but its that difficulty that keeps you coming back for more!
Flash Point: Fire Rescue: This is another Co-op game like Pandemic (I think these may be the only 2 co-op games in my collection). This game oozes theme, and provides a great player interaction in order to go in and save all of the victims trapped within a burning building. Another game that I can't recommend enough, nothing bad to be said.
PowerGrid: This game is usually hit or miss with people. There is definitely an element of luck to winning this game, which can throw off some people, but it's easily taught, fairly well balanced, and really a great time with the right group of people. It's based on an auction system, if you haven't tried an auction style game, give this one a go.
Quarriors (and its expansions): This game is just great fun! It's very light, and easy to learn, quick to play as well. This game has amazing player interaction, and gives you the opportunity to really partake in some serious dice rolling action, definitely a must have for any casual game night.
Race for the Galaxy: For those who like the Sci-Fi/Space theme, this is a great game. It takes a bit more time to learn and teach, but in my opinion is worth the time to learn, great stategy involved in the game. Perfect for people who love to plan out their strats and turn the tables on their opponents.
Small World: Light fun strategy game, lots of big swings of power throughout the game, one of the games where you can come from behind by making some good choices in mid game on your race/ability combos.
Ticket to Ride: A very accessible game for new comers to board games. Simple concept, some strategy, easy to learn and fun to play, definitely a strong gateway game to get players into some more involved/serious board games.
Citadels: Another fairly quick game, very strategic, great player interaction, well themed. Something we use to relax between the heavier games.
Telestrations: Great family game with the right people, basically the Telephone game re-imagined into an almost pictionary esque game. Lots of fun with a larger group of people.
Bang!: Offers a ton of player interaction, great theme, easy to pick up and lots of replay value, generally fairly quick games, and great with larger groups as well.
There's a ton more out there that are worth your time as well, unfortunately I'm not at home to go through my collection, so that's what I came up with off the top of my head.