Edited for more details, but be sure to visit Boardgamegeek for far more comprehensive info:
Apples to Apples - 1999 Mensa GOTY, fun party game as long as you're not playing entirely with vulcans and are good and playing the players. You're dealt a hand of words and a player is the judge, he displays his word and you have to quickly play a word that you feel you can justify as being the best match (slowest player doesn't get to play a card). The words are turned over and an open discussion takes place over which word best matches. That's it? Yep. Deceptively simple though, once you've tried it you'll understand. The Apple Crate (base game and expansions) can be had quite cheaply.
Speed Scrabble - Toss out the board and play on the floor (mix in two or more scrabble tile bags if you want). Most fun in teams. Tiles are facedown in a pool in the center, each team is dealt a hand of 7 tiles. As soon as you use all your tiles to make words that link in crossword/scrabble fashion (or just one 7-letter word), you call out "Tile!" and all teams draw a tile. If no team can use all their tiles, they agree and just draw another tile. You can break down and rearrange your puzzle anyway you want, just keep using up each new tile you get. The game ends when a team calls "Tile!" first and there are no tiles left.
Squint - Another game by Out Of The Box (Apples to Apples creators). You get a word then must use cards with various designs on them to get the others to guess the word. Easier and quicker than Apples to Apples.
Go - Very interesting game, a little over my head, but enjoyable if you try to win but don't take winning too seriously.
Chess - Well you know...
Citadels - Nice card game heavy on theme with variable player powers and bluffing. Can drag on with a too many players, but because of the theme, gets players into German games pretty easily. You try to built a citadel, each turn manipulating a different power player (Assassin, Priest, Warlord, Thief, Merchant, etc.) while trying to stop and guess what your opponents are using.
Bang! - Another theme-thick game. Scales well from 2 to 7 players. Variable player powers and bluffing and hand management. Takes place in the wild west. You get a public character with various powers and a secret role (Sherrif, Deputy, Outlaw, or Renegade) then, basically, try to kill the right people. Inexpensive and travels in the pocket. If your circle of friends even marginally likes westerns they should have fun.
Set - Just try it online
www.setgame.com
Carcassone is a hit or miss despite being quite inexpensive and heavily hyped. Game Keeper had clearances where they were getting rid of a boxed set that included the base game and most of the expansions for less than $20. Still, after a few playings, it got a little stale since it came down to luck, tile memorization, and slightly annoying farm scoring. I know plenty of people love this one, but I think this is a "try before your buy" game. Try the
demo version first.
If you have fun with these lighter German-styled games, you might want to try your hand at the more complex and expensive games like Settlers of Catan, Puerto Rico, Ticket To Ride, etc.