Yes, workers' compensation laws require an employee (or his or her family) to file a claim for workers' comp benefits within a certain amount of time. Each state has their own state-specific workers' comp laws, and some state's "statute of limitations" (deadline) for filing a claim depends on the type of injury. Typically, however, you will be safe if you file for benefits within one year of the date of your injury or accident.
There is another deadline involved with workplace injuries, however, and that is notification of your employer. Generally, you have to notify your employer within 30-45 days of being injured, or you can lose your right to file a workers' comp claim. This notification can be formal, such as sending a letter or email saying that you cut your hand on a piece of equipment, or informal, such as mentioning to your boss that your wrist hurts. It's safest to notify your employer in writing, and include the date and place of the accident or injury.
Learn more about when to report a workplace injury or illness that developed over time.