Dominion created an entirely new genre of game: in-game deck-building. It went through years of development, and it shows, having been polished to a mirror finish of rock-solid, pure gameplay. A theme has been pasted on top, but it's only skin deep.
Dominion is about a minor medieval lords expanding their small domain through careful economic work. They compete to have the largest, most noteworthy lands.
Each set of Dominion comes with a number of sets of cards representing money, victory points, and special cards. Some, like the core victory points and the money, are used in every game. A subset of the others are selected, usually at random.
Each player maintains their own deck. At the start it contains a few victory point cards and some low value money cards. On their turn a player draws a hand, plays a special card, and can spend money to purchase another card to add to their deck. Special cards allow a variety of special cases, including playing multiple cards, making more than one purchase in a turn, putting cards worth negative points into another player's deck, and more.
Eventually several of the available types of cards will be sold out, at which point the game ends. Each player then counts the victory point cards in their deck. That is their final score.
Gameplay is largely solitary, with little to no interaction between players depending on the cards available for purchase.
Dominion is an inspired bit of game design. One of the best parts of collectible card games (CCG) is deck building. Unfortunately it's a solitary activity, and one that tends to reward people who can spend lots of time and money looking for combinations. To try and solve this, many CCG fans participate in "draft" tournaments, where players select cards from a random, shared pool, forcing players to improvise and to make cost-benefit trade offs.
Dominion manages to capture the best parts of deck building in a 30 minutes. Everyone has the same pool potential cards to play with. Acquiring new cards is done throughout the game, seamlessly blending construction and gameplay. The subset of cards available for purchase varies from game to game, ensuring that each game is a new challenge.
The victory point cards are also cleverly connected. The common ones provide absolutely no benefit during the game. The special ones provide a benefit, but not in line with their cost. As someone purchases more and more victory point cards, the hands they draw end up with these deadweight cards. This tends to slightly slow down players with the most points, leading to satisfyingly close games, even between skilled and new players.
Because there is no shared state between players, players can plan while one of them is actually playing. Turns tend to be very fast, especially during the start when player's have limited options. Players will have lots of turns, but the game still ends in about 30 minutes with experienced players. New players might find that games take 45 minutes for their first game or two.
In game design there is alway a tension between theme and gameplay, a divide that shows in the eurogame versus ameritrash spectrum of gameplay. (Of course, ignoring the extreme purity of abstract games that do entirely without theme, games like Go.) Dominion falls solidly on the eurogram side of gameplay. The years of testing and development show. It's clear that each individual card was designed to provide a good gameplay experience, and if the theme doesn't quite hold up, so be it. Why does a Feast allow the player to purchase a card for free? Why does a Throne Room allow another card's power to be used twice? They're both well balanced cards, so it doesn't matter.
If Dominion has a problem, it's that the players don't interact much, and what interactions they have are indirect. It has been accused, fairly, of being multi-player solitaire. In many games the only interaction will be when a particular type of card sells out, denying it to others. Otherwise interactions are largely limited to occasionally putting negative victory point cards in someone else's deck, or forcing them to play a hand with 4 instead of 5 cards.
The Dominion series of games are great. I've played several dozen games and look forward to more. My views on the individual sets vary:
The original Dominion got everything right for a debut. The rules are at their simplest but it still has much emergent complexity. If there is a theme to the set, it's the ability to chain cards together. With skill and luck, it is possible to play card after card that give the player the ability to draw more cards and to play more, eventually cycling through their entire deck in a single turn.
Dominion: Intrigue is a good incremental step forward. More cards of the same quality as the original. The theme is slightly more complex cards, but the game plays very similarly. Intrigue adds victory point cards that have benefits in play. Intrigue can be played alone, and stands up well to doing so.
Dominion: Seaside is fun, but with this expansion things get more rough. While normally a player's entire hand is discarded every turn, Seaside adds cards that linger from turn to turn. The cards are colorful and give Dominion a very different feeling, but can feel unbalanced. In particular, the Pirate Ship is, for Dominion, a very aggressive attack card that can entirely change the flow of the game, giving the first mover a major edge.
Dominion: Alchemy isn't a bad expansion, but the complexity it adds doesn't feel worth it. Alchemy adds a new category of money: potions. This adds complexity to play, but the benefit feels dubious. Juggling two types of currency adds a bit of fun, but it doesn't feel in line with the added complexity. It also means that if you add Alchemy to your game, you really need to add a healthy dose of Alchemy or the secondary currency won't pay off.