A lot us play 2-player Dominion almost exclusively, because that's the fastest way to play, especially on the internet. In real life, I prefer 3-player, because it has a bit more interaction. Switching from 2 to 3 player takes some adjustments though and I'll talk a bit about them here.
Accelerated Junking
The problem with Cursers, Looters and other junkers in 3-player is not in the amount of crap you take in. A 3-player game has 20 Curses, while a 2-player game has 10. So on average you will get 6.7 Curses in 3-player to 5 in 2-player. That's not a big difference. The main difference is in the number of turns it takes for you to acquire a critical pile of crap. A 2-player game may take a good chunk of the middle-game to run out the Curses and you receive on average about 1 Curse per shuffle. This is why even a slow trasher can work in 2-player if there isn't a way to run out fast after the Curses are gone. With 3-player you get on average 2 Curses per shuffle and this will ruin your deck so quickly that you need to have quite strong trashing to outrace it. A single Salvager only for Curses isn't going to do much. On the other hand, because everyone's deck is so crappy, you might just have time for slow trashing. You just have to have a plan for a deck that will turn pretty bad, pretty quickly.
Piles, piles, piles
This is an obvious one, 3-pile endings will be a lot more common, but what you really have to take into consideration is that you can't get as many cards from a single pile as you would in 2-player. The average for action cards is 3.3 to 5 in a 2-player game. That's a significant difference. A Hunting Party stack doesn't work quite as well with 3 Hunting Parties. What does this mean? Mono-card strategies like Minion, Hunting Party, etc, are all going to do much worse. Of course it doesn't hurt to add such cards, but you shouldn't build your strategy around them. I wouldn't say BM is the obvious way to go, but money is much more important in 3-player.
Attaaaaack!
There are some attack cards that become significantly stronger with 3-player, the ones that attack other players' decks: Pirate Ship, Noble Brigand, even Thief and of course Jester. Your odds of hitting something good are just that much greater. Hand attacks like Militia are less of a big deal. Often one of the players already has 3 cards from a previous Militia and then you're really only attacking one player. Torturer is a special case here as it's even more brutal.
Deeeeefense
Well, we talked about attacks, so it's logical to talk about defense. As the chances of you being attacked are now doubled, defense is often a solid option. If a Moat can stop 2 Curses coming in on a single turn, that's as good as Gold! Most reaction cards are decent if there are attacks around.
Victory Piles
There are 12 cards in every victory card pile, so the average is still 4 per player. Why does it matter then? Well, because you can go for an alternative VP strategy and be able to get more cards from the pile than you would in 2-player. Duchy/Duke, Gardens, Silk Roads all become more interesting if you can get 6 of them instead of 4 or 5. You can also create more time for these strategies by forcing your opponents to get 6 Provinces each instead of 4. Keep watching for piles, of course.
Do Engines Still Work?
Well, that depends on the type of engine. A single- or two-card engine becomes much harder to pull off, simply because you can't get enough cards and the game will likely be over pretty fast if you do. You need a lot of variety and a couple different piles to incorporate into your engine. These kinds of engines are also the most fun, so when you can go with a 3-player engine that works, it can be really rewarding.
Scramble and Control
One thing I've noticed is that 3-player games are mostly a scramble for points. This is partly because you have less control. Sometimes you can control a 2-player game almost perfectly, but this is often simply not possible in 3-player. Another player may end the game while he and you are both still behind. So grabbing a lead is pretty important. With an early $8 I might just go ahead and get that Province over a Gold, taking these opportunities is just so important. Switching to Duchies can be done a lot earlier, all just to put yourself in a position to win when piles are drained.
Parting Thoughts
Switching from 2 to 3-player takes some adjustments. You have to keep in mind that the amount of interaction is doubled, there are now 2 players interacting with you and you are interacting with 2 yourself. This causes some attacks to have a much bigger impact. On the other hand, the average number of cards per pile influences your engine possibilities and the length of the game. Be aware that there are now 12 VP cards to get and adjust accordingly.