John signs a contract with Jane to buy a car, but he forges Joe's signature. Obviously, Joe isn't bound to the contract (at least, if he can prove he didn't sign it). Is John bound by it?
The signature is a formality indicating the existence of an agreement between two parties. There does exist an agreement between John and Jane, though John is poses as another person (for no obvious reason). Using a different name in an agreement does not render the agreement invalid, it simply complicates the question of enforcement if John wants to get out of the contract and claims that he never agreed to the transaction. Joe can proffer evidence (such as Jane's testimony) proving that he did not agree to the transaction. Jane can likewise proffer evidence proving that Joe did agree to the transaction. If the court concludes that Joe most likely did agree to the sale, it will conclude that he is bound by the contract, forged signature and assumed identity notwithstanding.
It depends on the circumstances
It’s possible for John, Joe, neither or both to be bound to the contract depending on the relationships, history, intention, who is seeking enforcement, and other circumstances.
To give just one example, if John and Joe are business partners then the act (wrongful of otherwise) of one of them binds all of them. In that case, if Jane seeks enforcement she can seek them from either or both of John and Joe.
No the actual signer of a forged document is not bound by the forged signature. However, the forger is probably liable for damages from the forgery, as well as guilty of committing forgery, a crime that could be prosecuted.
Typically, if someone gets caught forging a document, that person is considered criminal and the transaction will cease. If it has already gone through, the criminal is going to be liable for actions prompted by such falsehoods.
Intent to defraud means that the person had no intention to keep legitimate his/her signatures, therefore the contract will typically be cancelled.