Haggler is the better +Buy. With +Buy, you can pick up an extra card, but must split your money; good cards with +Buy require a lot of money to get a benefit from the +Buy. Haggler can get you a $4 and $3 with just $2 additional in cash, or a Province and a Gold with $6 additional in cash. This works well with many different types of decks.
General UsesHaggler reduces the stalling when you start greening. You can gain a Gold or Grand Market with your Province, keeping your money density up, or gain a card such as a Laboratory which lets you play extra cards to compensate for the dead card.
Haggler works well with expensive cards, and the ability to buy them. In Platinum/Colony games, if you have $11, you can get a Colony and a Platinum rather than needing to choose one. If you have $7 and can buy a Bank or an Expand, adding a Gold makes for a much better deal. If your hand is full of Curses and you need the Haggler to reach $3, the extra $2 card or Copper won't help much.
Haggler can also be useful for three-piling without losing VPs. If you are trying to end the game on piles and the third pile costs $4 or less, Haggler allows you to buy the Duchy you want and still exhaust the third pile.
Deck typesIn an engine, Haggler lets you pick up an extra component every turn, as long as you have components with different costs. You can get a Village with your Smithy, a Worker's Village with another Haggler, an extra Haggler with your Gold, a Conspirator with your Bazaar, or a Hamlet with almost any purchase. Multiple Hagglers, or Hagglers with +Buy, allow you to build the engine even faster. When your engine buys a Province, you can pick up another engine card, keeping the engine tuned up; thus engines with Hagglers can start buying Provinces a bit earlier.
In a big money deck, keeping your money density up is important at the end of the game; gaining Gold with your Provinces and Silver with your Duchies helps keep your ability to buy more greens. To get a mid-game benefit from the terminal Haggler, you need non-terminal $4 or $5 cards, as you don't want too many terminals in a big money deck. If you don't want any $4 or $5 cards, then Haggler gaining Gold will only add another Silver, and turns with $4 will force you to buy a terminal unless you want Silver and Copper. (With $5, you would probably choose not to play
the Haggler, or buy a Duchy and Silver.)
In alternate-VP rushes, keeping your money density up is even more important, as you will have more VP cards, and Silvers are enough for you to keep buying VP cards. Haggler is best with Gardens and Feodum; not only can you gain a Silver with these cards to keep from stalling, but the Silver also increases the value of the VP cards. You can also use it with Fairgrounds to get the $4 and $5 cards you are missing; the fact that you cannot take Gold as your extra card is likely to be irrelevant, as Fairgrounds decks do not need much Gold. And even though it doesn't directly help Silk Road or Duke, those decks need a lot of VP cards, and Silver keeps them going.
WeaknessesYou cannot take a Victory card (except indirectly if Haggler gains Border Village), so Haggler is no substitute for a +Buy when you want three Provinces on one megaturn, and it doesn't help when the second card you want is a double-type Victory card such as Island.
You cannot gain two cards of equal value; this can be a problem if your engine components all have the same cost (such as Worker's Village/Caravan/Smithy or Bazaar/Laboratory/Rabble). One-card engines (Hunting Party) may still work; you gain Hunting Party as your second card with Gold or Province, and gain some lesser card with Hunting Party.
Haggler doesn't work as well with Potion-cost cards, as the only less expensive cards are either other Potion-costs (and you cannot take Vineyard) or low-cost cards. Some combinations of Potion-cost cards will still work well, such as Alchemist/Apothecary, but Apothecary, Scrying Pool, and University will force you to take a Transmute or a Copper unless there are $2 kingdom cards. (Vineyard is still worse, as Copper and Curse are the only cards costing less than it, but you have no need to play Haggler when buying a Vineyard unless you have a +Buy and are haggling the other card.)
And the card gain is mandatory; buying a $3 card with Haggler may force you to take a Copper if there are no useful $2 actions, and some engines with no card under $4 may be stalled if you must take a Silver with your $4.
Watch out for three-piling with Hagglers around, as the cheap piles will get taken. If there are Hagglers but attacks are leading to weak turns, then $3 and $4 turns with Hagglers will exhaust the $2 and $3 actions. And if there are high-demand $2 or $3 cards (Fool's Gold, Fishing Village, Lighthouse with attacks around), they will go quickly as second cards with Hagglers.
You do not gain additional extra cards if you Throne Room or King's Court a Haggler, but mutliplying the $2 bonus is still valuable, as the bonus can add to the value of your extra card, so this is not a major weakness. KC/Haggler gets you at least a Gold and another Haggler, and with just an extra $2, it gets you a Province and another King's Court.
OpeningsHaggler is a reasonable opening with a 5/2 start, although it isn't as good as the powerful attackers. If the only $2 cards would conflict with Haggler (such as Moat or Secret Chamber), it's probably best to pass on the $2; if you need the $2 for defense, you should have bought the attack rather than the Haggler. (Haggler/Lighthouse is still good, as they do not conflict, and you gain the defensive benefit from the Lighthouse.)
Councilroom says that the strongest opening, other than the obvious Chapel, is Haggler/Haven. If you have both in hand, you can choose to use the Haggler this turn or next, whichever is better.
Synergies/CombosAlternate VP, particularly Feodum and Gardens
Most engines
Non-terminals at $4 and $5
Royal Seal/Watchtower (to top-deck both parts of a combo)
AntisynergiesMegaturns without +Buy
Engines with all components at the same price
Potion-cost cards, particularly $2P
Powerful attackers (cursers, Ambassador) leading to weak turns