There is a very limited array of exceptions in which a court will not enforce an arbitration agreement. The major exception is something called "unconscionable adhesion contracts." If a party does not wish to arbitrate and wants to convince the court that he shouldn't have to because the contract and/or arbitration clause was an unconscionable adhesion contract, there are a few key things he has to prove:
He must prove there was no reasonable opportunity for any sort of negotiation, and that the contract was presented to him on a take-it-or-leave it basis. This is the essential definition of an adhesion contract. Many contracts are adhesion contracts, like those for the purchase or use of airline tickets, insurance, cars, credit cards, cell phones, or any other consumer goods where you may sign a contract or agreement.
He must prove the terms were extremely unfair/unreasonable/advantageous to the party offering the contract. Essentially, this is what it takes to prove the terms are "unconscionable."
If the court doesn't find that a contract was an unconscionable adhesion contract, they will enforce the arbitration clause, and the two parties will have no choice but to handle their issue in arbitration. Further, whatever decision the arbitrator makes will be binding on both parties, unlike in other types of alternative dispute resolution (ADR) like mediation.