Sometimes, you just want to get the incident behind you. But resolving a claim too quickly could mean an inadequate settlement.
Generally, for injuries where pain and damage can linger, don't settle until the point of maximum medical improvement. With other types of claims (such as fire, where you might not be certain of the property loss), give yourself time to gather all the necessary information. Then take time to consider the offered settlement to determine if it's fair. If not, go back to the insurer.
Remember, insurance is not for a quick cheque, "it's to reimburse you for what you've lost," says General Insurance OmbudService's Maltman.