Nobles Nobles combine very well with themselves, or with action multipliers like Throne Room, King's Court or Golem.
boardgames.stackexchange.com/users/318/Andrew Vandever
The dominion strategy blog has a bunch of interesting combos.
My favorites are: Black Market/Tactician
: Use the black markets ability to play (not neccesarily even spend!)
your money before the buy phase, to subvert the tacticians "throw away your hand" downside.
You got to keep your money AND play the tactician!
Ambassador/
Curse : After you get your deck small, intentionally buy a curse to "upgrade" your ambassador into a sea hag!
Quarry/Talisman :
Talisman lets you gain an additional card when it costs <= 4.
Quarry reduces action costs by 2.
Play a Quarry and Talisman together and for a single buy of a six cost action for $4, you get an additional one.
boardgames.stackexchange.com/users/322/rrenaud
I'm a fan of the Scout combos:
boardgames.stackexchange.com/users/560/Pithlit
With any other multiple action card: 5 Victory point tokens for trashing a card that could cost you nothing if you played 4 actions: No, seriously, the possibilities are endless.
There's a reason why card randomizers are so common... so that you play with a different set of 10 cards of the 112/115 available cards each time.
boardgames.stackexchange.com/users/87/Powerlord
I feel like posting more combinations.
boardgames.stackexchange.com/users/87/Powerlord
Just a couple I've encountered recently:
Treasure Map +
Watchtower - being able to put new Treasure Maps on top of your deck in the early game significantly improves the odds that you'll get two in your hand.
Counting House + Cellar - discard all your Copper, draw replacements, then put the Copper back in your hand.
Herbalist + Platinum - really, this is just obscene.
Scrying Pool + City - the Scrying Pool is so weak, and so cheap, and so horribly effective if you've got a lot of Cities in your deck.
Oh, and I forgot: Counting House +
Vault - sure, you need +1 action to pull this off, but at a minimum it makes all the copper in your hand worth double.
Contraband + Gardens - especially if your opponent doesn't think to ban you from buying more Contraband with your Contraband.
It's not hard to average 3 cards a turn with this.
boardgames.stackexchange.com/users/162/Robert Rossney
What happens when Golem fails to find two action card apart from other Golems?
Your entire deck (minus your hand) is discarded.
What happens when Golem finds one Counting House and nothing else?
Every single Copper in your deck comes into your hand.
Buy one Counting House, several Golems, and an extra Copper (or four, if you're going for Colonies), and you're guaranteed a Province every turn you have Golem and no Counting House in your hand.
It gets boring after a bit, but, man, is this combination fun to pull on your friends once.
boardgames.stackexchange.com/users/78/keithjgrant
When you are trying to cash in Treasure Maps, use Chancellor to reshuffle your deck if you missed the pairing.
boardgames.stackexchange.com/users/78/keithjgrant
Buy a Tactician and a few Banks.
I just discovered this one yesterday; combined with a Festival
, I was able to buy three Provinces in one turn, and still have change left over for a smaller card.
boardgames.stackexchange.com/users/78/keithjgrant
I have not personally pulled this off
but I have seen this in action - in which, you can use a Remodel card to remodel a remodel card so that you can increase your costs to gain a card of a higher value.
This is a very slow process but it can come in pretty handy when there are limited avenues of income within a very thin deck.
boardgames.stackexchange.com/users/466/Michael Feng
I've only played a few games of the base set, but I already noticed some very powerful combinations:   Laboratory can be repeatedly combo'd with itself to draw a massive amount of treasure from your deck early in the game.  Remodel can be used on Gold to quickly convert it to provinces during endgame.   Share your favorite powerful combinations.
What are the most effective action combinations in Dominion?
boardgames.stackexchange.com
<dominion>
boardgames.stackexchange.com/questions/1321
boardgames.stackexchange.com/users/369/Marcin
Counting House + Cellar, Herbalist + Platinum, Scrying Pool + City, Contraband + Gardens. You can play a Quarry and Talisman together and for a single buy of a six cost action for $4, you get an additional one. Counting House + Cellar - discard all your Copper, draw replacements, then put the Copper back in your hand.  The Herbalist + Platinum is a great combination, as is Scrying Pool + City, because Scrying Pool is so weak and so cheap, yet extremely effective if you've got a lot of Cities in your deck.  Contraband + Gardens is useful if your opponent doesn't think of banning you from buying more Contraband with your Contraband.  
If you buy one Counting House, several Golems, and an extra Copper, you're guaranteed a Province every turn you have Golem and no Counting House in your hand.  When you are trying to cash in Treasure Maps, use Chancellor to reshuffle your deck if you missed the pairing. You can use a Remodel card to remodel a remodel card so you can increase your costs to gain a card of a higher value.  
You can play a Quarry and Talisman together and for a single buy of a six cost action for $4, you get an additional one.  S2: Watchtower - being able to put new Treasure Maps on top of your deck in the early game significantly improves the odds that you'll get two in your hand.   Counting House + Cellar - discard all your Copper, draw replacements, then put the Copper back in your hand.  The Herbalist + Platinum is a great combination, as is Scrying Pool + City, because Scrying Pool is so weak and so cheap, yet extremely effective if you've got a lot of Cities in your deck.  Contraband + Gardens is useful if your opponent doesn't think of banning you from buying more Contraband with your Contraband.   If you buy one Counting House, several Golems, and an extra Copper, you're guaranteed a Province every turn you have Golem and no Counting House in your hand.  When you are trying to cash in Treasure Maps, use Chancellor to reshuffle your deck if you missed the pairing. You can use a Remodel card to remodel a remodel card so you can increase your costs to gain a card of a higher value.  