My Current Favorite 5 games (constantly changing):
Dominion - Maybe the perfect game. You use your resources to build the best deck possible to grab the victory points before your opponents. Any given game you use only 10 of the 25 action cards, making every game different. Strategy changes based on which exact set of 10 action cards the game has in play. Can play 2 player, which is a plus over games like Settlers. I play this on brettspielwelt. BGG Rating: 8.06
Settlers of Catan - Superior to Risk in every possible way. Build your settlements on strategic resource locations. As you gain or trade resources, use them to build roads and build more settlements, which mean more resources. Build largest army or longest road for 2 more victory points. Play to 10, 13 or 15 victory points. Awesome game for 3-4 players. Great with 5-6 as well, but must buy the expansion to do so. I play this on games.asobrain.com. BGG Rating: 7.64
New World: Carcassonne - I've only played this version, not the original, which has better rating. It's a tile-building game where you build the game board together as you go and you try to deploy your resources and arrange the tiles to maximize your chances of winning. Plus for being able to be played by 2 players. BGG Rating: 6.58
Set - Every card has 4 attributes: Color, Shape, Number, Shading. Each attribute has one of 3 states. The community game board is just 12 cards placed on a table. First one to find a set calls SET and then picks it up if right. Deal 3 more cards. To make a set, all 4 attributes on the 3 cards have to either match or be unique. So all 3 cards can be red, diamond, filled in with one card having 1 diamond, one having 2 and one having 3.
Here is a place to do a daily Set puzzle. Go there to better understand the game in just one minute. BGG Rating: 6.49
Zombie Fluxx - Just a fun game. More tactical than strategic. Only 2 rules: draw a card, play a card. But new rules get added and the goal to win constantly changes. Drawback - due to the nature of the game, you never know if it will take 5 minutes or 45 to finish. BGG Rating: 6.39
i'll add other favorites as the thread goes on