+Buy
Playing a card that provides +Buy increases the number of cards you are allowed to buy during your buy phase.
Some cards that give +Buy have it as part of their core function, such as Herbalist; usually the +Buy is the only reason for wanting a Herbalist. In some cases, a card offers +Buy as a feature that synergizes with its core function: Collection offers you a 
reward per card you buy, and gives +Buy to make the reward go farther. Other cards have +Buy merely as an extra vanilla bonus that keeps the card competitive with other cards at the same cost: Worker's Village is a village costing 
with the +Buy as an extra bonus for the 
it costs more than Village.
Strategy
+Buy is an essential component of most engine strategies, since engines can take a long time to build; +Buy allows you to acquire engine components more rapidly, thus speeding up the construction of the engine, and once the engine is running it allows you to buy multiple Victory cards at once to make up for the slower start. An easy trap to fall into is that of "overbuilding" an engine in the absence of +Buy: there's no use in building a deck that can regularly generate 
each turn if you can still only buy one Province with it. In some cases, if the +Buy card is rather unwieldy like Herbalist, it is good strategy to wait to buy even a relatively cheap +Buy card until you are close to generating enough 
to benefit from the effect, although you need to avoid waiting too long as well or else you will have to waste on the turn you buy that card.
If you are lacking the deck control to generate large amounts of or to assure having a +Buy card in hand when you do, a +Buy card may not be worth its opportunity cost.
Cards that give unrestricted +Buy
Cards in italics have been removed.
Terminal coin or the equivalent
- Dominion: Woodcutter
- Intrigue: Baron, Bridge
- Alchemy: Herbalist
- Prosperity: Goons
- Hinterlands: Nomad Camp, Nomads, Souk
- Dark Ages: Storeroom
- Cornucopia & Guilds: Horse Traders, Merchant Guild
- Adventures: Bridge Troll, Messenger, Peasant, Wine Merchant
- Empires: Farmers' Market
- Nocturne: Druid, Sacred Grove, Skulk
- Menagerie: Way of the Monkey
- Allies: Herb Gatherer
- Rising Sun: Fishmonger
Terminal draw
- Dominion: Council Room
- Seaside: Wharf
- Hinterlands: Margrave
- Dark Ages: Storeroom
- Adventures: Ranger
- Nocturne: Tragic Hero
- Renaissance: Silk Merchant
- Menagerie: Barge
- Allies: Marquis
- Plunder: Figurine
- Rising Sun: Imperial Envoy
Cantrip
- Dominion: Market
- Prosperity: Grand Market, Worker's Village
- Dark Ages: Market Square
- Cornucopia & Guilds: Farrier, Hamlet
- Menagerie: Sanctuary, Snowy Village
- Rising Sun: Gold Mine
Treasures and other non-terminal stop cards
- Dominion: Festival
- Seaside: Astrolabe
- Prosperity: Collection, Tiara
- Hinterlands: Cauldron
- Dark Ages: Counterfeit
- Cornucopia & Guilds: Candlestick Maker
- Empires: Capital, Fortune, Villa
- Nocturne: Pouch
- Renaissance: Ducat, Spices
- Menagerie: Stockpile
- Plunder: Buried Treasure, Jewelled Egg, Mining Road, Rope, Sack of Loot
- Loot cards: Amphora, Endless Chalice, Jewels, Orb, Prize Goat, Puzzle Box, Sextant, Shield, Staff, Sword
- Rising Sun: Good Harvest, Rice
+Buy with a choice of other options
Other
- Travelling Fair can transfer arbitrary amounts of into +Buy
- Seaway and Teacher can give +Buy to an Action card pile in the Supply.
- League of Shopkeepers can give you +Buy when you play a Liaison.
- Flourishing Trade can convert excess +Actions into +Buy
Cards that give restricted +Buy
Cards that need to trash a card
Some cards need to trash or return a card, so they only replace cards.
- Seaside: Salvager
- Prosperity: Trade Route
- Hinterlands: Spice Merchant
- Dark Ages: Forager
- Rising Sun: Panic
Limited amounts of +Buy
Some cards are difficult to come by, only exist in very limited numbers, or only provide a limited number of +Buy in normal circumstances.
- Seaside: Tactician
- Dark Ages: Ruined Market, Sir Martin
- Cornucopia & Guilds: Demesne, Princess, Renown
- Nocturne: The Forest's Gift
- Renaissance: Fair
- Rising Sun: Aristocrat
Other restrictions
Some cards only work later during the game when one or more piles have emptied.
Contraband and Deluded
can prevent you from buying certain cards.
Some effects need you to to gain specific kinds of cards to get +Buy:
Giving back Buys
Forum, Cavalry, Marchland, and Nearby cards give +Buy when gained. Similarly, Villa can be played instantly after being gained and so gives back a Buy.
Galleria and Band of Nomads can give back Buys upon buying certain cards.
A number of Events do not use up a Buy because they give one back whenever bought.
- Adventures: Borrow, Save, Scouting Party
- Empires: Delve
- Menagerie: Desperation, Gamble, Pursue, Toil
- Plunder: Avoid, Bury, Deliver, Launch, Mirror, Rush
- Rising Sun: Continue
Related
Cards that do not give +Buy per se but enable you to gain more cards through Buys in some other way are referred to as Virtual +Buy.
Gallery
Terminal
Terminal draw
Cantrip
Treasures and other non-terminal stop cards
+Buy between other options
Other unrestricted +Buy
Cards that need to trash a card
Limited amounts of +Buy
Other restrictions
Giving back Buys
Removed cards
