Take out the Trash
* I'm bored.
* I'm in a writing mood.
* I'm in a gaming mood.
* I have an idea of something worth writing.
This is understandably very rare, but whatever. I just can't abandon it.
For the record, the deckbuilding games I've played significantly include Dominion, Star Trek, Nightfall, and Puzzle Strike. All of these games involve a trash element, and it's deeply important in all of them (perhaps most in Puzzle Strike, where you are forced to get something new each turn).
So, what's the point of trashing? It's largely about probability. For example, in Dominion you get 7 cards that produce money and 3 that are, at this point in the game, completely useless. Since you draw 5 cards and 3 of your 10 cards have no practical purpose, chances are high you'll draw one of those. That means you're effectively drawing less cards. What if you simply didn't have those blank cards? What if you got to draw all money all the time? You become a lot more productive. Let's move forward a bit. Let's say you've bought that trashing card and some more powerful money cards. Your starting money, Copper, provides $1, versus Silver and Gold that provide $2 and $3, respectively. Drawing a Silver is basically like drawing 2 Copper, but drawing a Copper is drawing 1 Copper. Copper is definitely not as productive to you. You want to draw the Silver more often and draw Copper less. Just getting more Silver is one way to do that, but getting rid of the Copper entirely is far more effective. If it doesn't exist, you'll never draw it, so you'll naturally draw the cards you want. As you start getting Gold, even those Silvers can be worth trashing for the same reason.
Yes, those cards you start with are important to get you off the ground, but as long as they stay in your deck, you still have them in your deck, you are forced to use them instead of your other, more powerful things sometimes. Simply put, trash cards give you the opportunity to outright replace your weaker cards with better ones. This much is obvious in cards like Remodel, but it's still there with cards that trash without changing the card.
Puzzle Strike throws a few special wrenches at you. In Puzzle Strike, you are forced to get a new card every turn. No other game I know forces you to get a new card. Star Trek even has the option of just trashing a card for your turn without needing to play cards if your hand is crap, and Nightfall actually forces you to trash your starting cards after you've played them. By constantly being forced to get something, your deck will often get clogged up with irrelevant things. Furthermore, the game is actively attacking you each turn, so you won't really get the time to develop like you normally would in other games. However, this makes trashing more important than in any other game. The need for efficiency is even greater; you just can't be as patient in your development.
Then there's the golden standard: the deck-hand. If you've trashed well enough, your deck should be so miniscule that it won't take much effort to get all of it into your hand. You can't accomplish this just with flooding your deck with card-drawing, because there's still a significant chance you'll draw a starting hand of basic filler. Once you can consistently draw your deck, you can start to concentrate on how productive the deck is vs. how likely you are to have a productive hand.