I was there at Carnegie Mellon's gaming club in 1994, ground zero for the explosion that was Magic: the Gathering. I witnessed people taking their paychecks down to the local game store and exchanging them for boxes of cards. I saw these same people begging others to take their boxes of old Commons that were useless. I saw people trying desperately to find ways to organize their collections so they could build a deck in some reasonable amount of time.
It turned out that collecting was fun, trading was fun, building decks was fun, playing was fun... but organizing thousands of cards into some coherent system was tedious and boring. Somewhere along the line I stopped bothering with it; it took too much time that was better spent playing games. If I play these days, it's with preconstructed decks... just so I don't have to think like a librarian.
Dominion solves this problem in a unique way. It's a standalone game where the players build their decks during play as part of the game.
All players start with the same ten-card deck: seven Copper cards (you can think of these as "basic land," you use them to buy things) and three Estate cards (which are completely useless dead weight in your hand... but each is worth a Victory Point at the end of the game, so they are also your victory condition).
Your turn is usually pretty simple. You can play up to one Action card (note that you don't start with any, so you simply decline to play one in the first few turns). Then, you lay down all of the treasure in your hand (such as Copper) and use it to purchase a new card for your deck. You can buy new treasure (Silver and Gold, which are like Copper but worth more), new Victory Point cards, or new Action cards. There are ten different types of Action cards available in the game; they let you do things like buy more cards in a turn, or draw extra cards, or upgrade your existing cards in addition to your normal purchase (or, naturally, slow down your opponents by forcing them to discard or inserting useless cards in their decks). Each card has a cost, so you can only buy what the treasure in your hand lets you afford. The new card goes in your discard pile, so you can't use it right away. Then you discard all remaining cards in your hand and draw back up to five. Your turn ends, the next player in turn order goes.
When your deck runs out, you reshuffle your discards to form a new deck. This happens a lot in the early game, but gets less frequent as you purchase more cards and your deck gets larger.
The cards available for purchase are in limited supply. When all of the most expensive victory point cards are gone, or when three Action card piles are gone, the game ends immediately.
As such, players are constantly tinkering with the mix of cards in their deck. Too many Action cards and you won't be able to play them all, and the rest are just dead weight in your hand; not enough Actions and your action phase is wasted. Too many Victory Point cards and you slow yourself down, too few and you can't win the game. Too many low-value Treasure cards and you'll never draw enough to buy the really expensive cards, too many high-value Treasure cards and you've spent all your resources on Treasure and not other things that you need. In short, you're trying to balance your deck to be the most powerful, while competing with everyone else at the table.
To keep things fresh, the game comes with 25 different kinds of Action cards. You only play with 10 each game, but a different mix leads to wildly different game dynamics. You can select from any of several suggested lists in the rules, choose your favorites, allow the players to do some kind of voting or draft, or just determine them randomly.
All in all, a very clever and streamlined TCG-like experience, for those of us who would prefer not to deal with the hassle of organizing a collection.