Dominion is a deck-building game where players acquire cards from a common set of supply piles in an effort to build the best deck (defined soon). There are three types of cards: Treasure Cards, purchasing power necessary for a player to acquire new cards; Action Cards, which give a player more draws from her deck, actions, buys, or purchasing power this turn (+Cards, +Actions, +Buys, +Money) and Victory Cards, which give the player victory points. When the game ends, the person with the most victory points wins. The game ends when three piles run out (of 17 or more) or when Provinces (6-Victory-Point cards) run out.
At the start of each turn, a player holds a hand with 5 cards, drawn randomly from her deck. From these five cards, the player may play one action card (more if the action card gives +Actions) and buy one card (more if an action gives +Buys) from one of the supply piles. Treasure cards used in the buy phase remain part of the player's deck. At the conclusion of the turn, all cards acquired and from the hand go into the player's discard pile to be shuffled together into a new (better) deck when the deck is exhausted.
Each game involves 10 Kingdom cards whose supply piles are made available to the players. Even in the standard deck, there are 25 Kingdom cards to choose from (3268760 possible games) Including all of the expansion decks, there are 157 possible cards. This means that there are 1871 trillion different possible games (Yes, 1.871*10^15). Because every game is different, Dominion never gets old.
My description merely scratches the surface. There are plenty of guides out there on the game. Here's a FAQ. Here are the official rules. What's even better? There's a free online version of the game, complete with a rather sophisticated ranking system.
Good dominion strategy involves making complicated tradeoffs. The piles are finite, actions and buys are limited by the rules. Given a hand and current deck, the amount of treasure is finite. With all of this scarcity, Dominion really makes players think consciously about opportunity cost. For all the complication, the game is surprisingly popular. Yesterday, the online site reported that nearly 15000 games were played through the interface. If you're a fan of games that make you think, give it a try.