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
- Throne Room / King’s Court
- Treasure Map
- Remodel / Expand
- Counting House
- Sets without +Actions
- Combinations of Actions in general
- 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.