Discharge by agreement

1. The contract may be discharged by mutual agreement (they agreed to be bound, so they can agree not to be). In this case, the agreement of one party forms consideration for the agreement of the other.
But if one party, having performed or being ready and willing to perform his part of the contract, merely waives performance by the other (i.e. agrees to postpone it) he can always retract the waiver by reasonable notice unless it has been supported by fresh consideration. Compare: Pinnel's Case 1602

2. An existing contract can be replaced by another, discharging the old one, upon mutual agreement (novation).

3. If a contract is subject to a condition subsequent (resolutive), failure of the condition may give rise to discharge.

4. A contract may also be discharged by accord and satisfaction - the creditor accepting something different instead of what has been owed originally.
However, the payment of a lesser sum of money will not discharge the debtor unless promissory estoppel can be invoked, or there is novation, or there is fresh consideration:
Pinnel's Case 1602

5. Contracts of indefinite duration require - either expressly or by implication - appropriate notice for their discharge.