On BGG, I've rated 436 games. Here are my top games, right now:
Bridge - The ultimate card game
Cosmic Encounter - The game where every game really is different, and every rule can be broken. The link is to a newer version of the game, which I haven't played. I am familiar only with the original EON and Mayfair versions.
Go - The ultimate board game (for two players)
Magic: the Gathering - A classic CCG, designed by a fan of Cosmic Encounter. A fantastic game, both for its deck-building and play experiences.
Puerto Rico - Possibly the ultimate multi-player board game, though it greatly benefits with a few building changes or a variable set of buildings.
Age of Steam/Steam - The best route-building train games. The first is decidedly heavier than the second.
Anagrams - The link is to Bananagrams, but that's not the game I'm referring to. To play Anagrams, pull tiles out (from Bananagrams or Scrabble) one by one. Call words whenever you see them to win the word. Steal or change a word by calling a bigger word using someone's existing word and one or more new letter tiles.
Antike - In my opinion, the ultimate RISK-killer, though I recognize that some people must have their dice-rolling; I can recommend a few RISK-killers for them.
Dominion - A game based around building your deck as you play from a common pool of cards. Using a limited number of available cards from an ever-growing pool of cards makes for infinite re-playability, and it's a great game, too.
Dvonn - One of two excellent abstract games from the GIPF series on my list, this is a game that you uncover slowly each time you play. It's quick and fun.
Homesteaders - A fantastic board game designed by a Puerto Rico fan, he has created a game that just may challenge Puerto Rico for the throne. It's accessible, with dozens of options and no clear dominating strategy (yet).
Le Havre - From the designer of the hit game Agricola, this is a much better sprawling epic of a Eurogame.
Netrunner - The other CCG on the list, this is an excellent game of hacker vs corporation, and almost always a tense, thrilling game (with occasional exceptional bad luck, which is why it's only a 9).
Pente - The second best thing to do on a Go board. Every once in a while I think the game is simple, only to discover new depths.
Princes of Florence - A tense, yet beautiful and serene auction game.
Santiago - Elegent, simple crop irrigation game.
Scrabble - One of the few modern games that has not diminished with age. Too many modern two-letter words break the integrity of the game.
Tichu - An excellent partnership ladder game (think President, but oh so much better).
Tigris and Euphrates - Knizia's true masterpiece, the rules are not difficult, but the implications of each rule and each play can be hard to wrap your head around.
Tikal - Beautiful game board, and a great game of jungle exploration using action points.
Trias - Appears to be insubstantial, but a wonderful light game of drifting tiles and dinosaurs, nearly abstract.
Tzaar - The other GIPF game, it has a lot of the same magic that Dvonn has.