Library is the most unusual of the +Cards Actions. Because you don’t draw a set number of cards, but rather up to 7, it responds poorly to Throne Room but does quite well with small hands (normally a drawback). Preferably, you get your small hand through disappearing +2 Actions cards (Festival, University); indeed, the synergy between Festival and Library are so strong that when Donald X. moved Festival into the base set, he pulled Library in with it as well to keep them together. It’s theoretically true that Library works well with Outpost, but the chance of drawing a +Actions with it in the 3-card hand is pretty small unless you’re Havening cards between hands.
Alternatively, Library is a fundamental “soft counter” to handsize-decreasing cards like Militia and Torturer. (In fact, its presence is often a strong deterrent to playing Militia, since it’s even better of a counter than Moat.) Library can also be used effectively with discard-for-benefit cards (Vault, Secret Chamber, even Haven), if you have enough +Actions to play it all: discard your cards, then redraw with the Library. And it’s possible — though unlikely — to use Golem for this purpose (ideally by drawing Tactician/Library).
Its benefit of setting Action cards aside is a little less useful than it seems. Obviously it’s of most use when your deck is cluttered with terminal Actions … but then your deck is cluttered with terminal Actions. It’s more often better used as a way to discard the outmoded opening Actions (e.g., Chapel, Moneylender), or as part of an endgame desperate draw, hoping to get up to $8. (Special note: sometimes you’ll want to set aside useless non-terminals like Great Hall; this is because it draws you a card, but without giving you the option of setting it aside or not.) Alternatively, it can be nice when combined with Scrying Pool, since Library can draw all your non-Actions, and Scrying Pool picks up the Actions.
Unsurprisingly, Library is quite terrible when your hand is already quite large. This means that not only does it anti-synergize with Laboratory, it also anti-synergizes with itself unless you are drawing more disappearing +2 Actions. But at least you can set them aside, which can be quite useful if you’re running a rote Smithy/Big Money strategy with Library in place of Smithy.
- Festival/University/Native Village/Nobles/other disappearing +2 Actions
- Vault/Secret Chamber/Haven
- Chapel, Moneylender, Trading Post, other “opening Actions” that are outmoded later on
- Opponents’ Militia, Torturer, Ghost Ship, and other handsize-decreasing attacks
- Black Market (in a similar vein as Black Market/Tactician, though this is admittedly difficult to pull off because you don’t have the extra Action from Tactician)
- Caravan, Tactician, Laboratory, other handsize increasers
- Throne Room (Throne Rooming a Library is much worse than Throne Rooming a Smithy)
- Itself, if you aren’t drawing disappearing Actions
- Opponents’ Council Rooms