Ah, Board Games. I have played many in my short years on this earth, more than most people my age have played. First off, what KIND of Board Game are you thinking about? Large-Scale play? One-on-One? Do you want a Board Game based on something, like a movie or licence, or no? And, when you say 'Board Game', does it necessarily NEED to have a 'board'? Would a structured Card Game suffice?
First off, the classics are just that: Classics. Monopoly, Sorry, Scrabble, Life; these games continue to be mainstays for 'Board Gaming'. Of course, these games can also get boring, which is why there are so many other, less-known games out there. In a way, Monopoly and Scrabble are like the Super Mario or Board Games; sure, it's still fun to play, but that doesn't remove the fact that it's essentially the same game over and over.
If you want something more 'new', I suggest a few games. First off, I'll recommend the game 'Zombies!!!' by Twilight Creations Inc. It's a really interesting game, played with 2-6 players. Essentially, the 'board' is actually made up of separate Tiles, which are drawn from a pool and placed on a table/flat surface. As the game progresses, the town get 'explored' and the board grows. The object is to make it to the Helipad (which will eventually be drawn and strategically be placed), or to kill 25 zombies, whichever comes first. There is a lot of back-stabbing involved with this games, mostly used with the Cards you draw to either screw over the other players or bolster your own survivor. It should be noted, though, that you will probably need a fairly large area to play this, as the board can get quite large, especially if you play with any of the 12 expansions.
If you don't necessarily NEED a 'board', I think a good alternative is a game like 'Munchkins'. One of my favorite games of all time, Munchkins is basically a card game that parodies old-school DnD. You could be a Gnome Warrior with the 'Boots of Butt-Kicking' or an Orc-Halfling Bard wearing a Fake Beard (thus getting treated as a Dwarf) wielding a Really Big Rock. This game relies more heavily on teamwork, or the lack thereof, than 'Zombies!!!' While you can assist another player (possibly for a reward; there 'aint no such thing as a free lunch!) you can just as easily backstab them by buffing up the monster he's fighting, or even throwing another monster into the combat. All in all, a game of Munchkins is a good time.
Now, I'm going to recommend this game mainly because I love it. I doubt you'd actually get it, as it's kind of an obscure game at this point. The game I'm talking about is "Escape From New York: The Game". Whether or not you like (or remember) the movie, the Board Game is pretty fun. Played between 2-4 players (though the more, the better) each player has to try to rescue the President, or retrieve the Recorder, and escape the city before the other players. Using gear cards, you can augment your abilities throughout the game. What's interesting is that not all of the 'enemies' you fight are hostile; you have a chance to convince many of the gangs (and some of the characters from the movie) to ally themselves with you, thereby strengthening you for further conflicts. All the while collecting clues to where the Recorder, or the President, is being held. However, this game has been long out of print, and should only be bought by those with either a long-love of the Movies, considerable means, or if you thought my endorsement was SO good that you were compelled to look for a copy (which I doubt. I mean, I'm not that good).
Lastly, I'll recommend any of the games from Cheapass Games, at www.cheapass.com. As the name implies, these games are cheap, and cost either very little, or nothing at all. These kind of games are for all those do-it-yourself-ers out there, since many of them require you to make your own Boards, Cards and pieces (following their directions, of course). This can prove fun, since you can always use that little figure of an Army Man with everything above the waist melted off as your game piece, or the cards just printed-out labels put on some of your old Pokemon cards you've been meaning to get rid of. And, though the game may be inexpensive, they are definitely fun.
In addition to the games I've listed, one thing you could do is visit a local hobby or gaming store and look around. Ask other people in the store what they like, and what they'd recommend. There are so many games out there, and so many favorites. Just keep looking!
