Dominion: Seaside
Haven is my personal second-favorite $2 card (after you-know-what). It significantly reduces the luck of the draw by allowing you to control card distribution. For instance, it allows you to shuffle the Explorer, Treasure Map, or Throne Room around in your deck until you find the right card to pair it with. But it also helps put together other combinations that more subtly depend on other cards: if you draw a Remodel with nothing worth Remodeling, a Smithy without +Actions, a Tactician with too much money, an early Counting House, or even a Lighthouse with another Lighthouse, then just use Haven to save it for later. In addition, in sets without +Actions, Haven can keep your terminal actions separate so you aren’t forced to discard one of them. It works especially well with Conspirator; not only does Haven feed the Conspirator chain, it also allows you to save an otherwise dead Conspirator for later hands that have more Actions to play.
Haven also optimizes Treasure distribution. Stuck at $7 again, without anything to buy? Haven away a Copper, and next turn it might push you over to $8. Drew a Platinum with too much money already without +Buy? Haven it away for a big turn next turn. Have $5◉, and unsure of whether to get the Familiar or a Laboratory? Haven away the Potion (or a Silver). And when you have nothing you want to Haven, you can always tuck away a Victory card.
Haven’s biggest drawback are situations where you have 5 cards that add up exactly to 8 (or 11), and you can’t Haven any of them. But that’s pretty rare. In addition, Haven’s power is less helpful if your deck is heavily attack-based or Duration-based, since those are typically cards that you always want to play at the first opportunity.
EDIT: see discussion in comments for a comparison of Haven and Courtyard, which are very similar
Works with:
- Throne Room / King’s Court
- Treasure Map
- Remodel / Expand
- Explorer
- Conspirator
- Potion
- Vault
- Counting House
- Sets without +Actions
- Combinations of Actions in general
Conflicts with:
- Actions that don’t depend on other cards, and which you generally want to play as soon as possible. For example: Spy, Witch, Mountebank, and Duration cards like Caravan or Merchant Ship.
Dominion Strategy 
I’m surprised that you put Haven at #2 over Courtyard. Courtyard has all the amazing draw-smoothing of Haven AND is +1 card instead of +0 cards — with Courtyard, you get a 6 card hand now followed by a smoothed 5 card hand. With haven you get a 4 card hand now followed by a smoothed 6 card hand. Getting the bigger hand sooner makes Courtyard even better – maybe you’re about to shuffle, or the game is about to end.
On top of all that, it’s not a duration, so you don’t get randomly duration-screwed with it. I can’t see how it’s not almost strictly better.
You’re right that Courtyard, in quite a few situations, is superior.
But I like Haven overall better for three reasons:
1) It’s free, Action-wise, which is important to me because I’m a jerk and enjoy playing Attack cards, which are usually terminal. (It also leads to a Conspirator chain and cuts Peddler cost.)
2) Playing multiple Havens is extremely effective, whereas you can’t play multiple Courtyards without +Actions, and even then it only top-decks one card for you next turn.
3) The two above reasons mean that you can spam-purchase Havens without worry, which is useful for Goons/Vineyards.
We had a crazy four player game where several people when Throne Room + Saboteur, and nobody could keep a card worth more than $2 in their deck or discard pile. Literally, if it wasn’t in your hand, set aside with the Native Village, or set aside with the Haven, it was destroyed. Guaranteed. Provinces would be bought, turned into Gold, which was turned into Silver before the purchaser got back to his turn.
The winner was the guy who bought a couple of Provinces before the Saboteurs really heated up, and hid the Provinces in in his alternating Havens every turn throughout the entire game.
I was that guy in a recent game. was quite proud of myself when my opponents realized what i was doing with the havens.
VAULT
You mentioned Tactician, but I think there’s more to be said — or maybe just the same thing over again with enthusiasm! ( :
The biggest drawback of the Tactician (obviously) is losing the chance to play the other cards in your hand. A single Haven ameliorates this somewhat, but a bunch of Havens work wonders. There’s nothing is more satisfying than tucking away ALL of your important action and treasure cards for next turn, and then playing Tactician last (remember to leave at least one card for a discard!).