It you are hit by a car and the other guy is at fault, then you potentially have two claims (1) the claim against the at-fault driver, and (2) the claim against your own car insurance company if the other driver does not have enough insurance to cover all your damages. (Click here for a discussion on uninsured/underinsured claims). The claim against the at-fault driver is a negligence claim, which means that the deadline to file suit is 2 years. However, the claim against your own insurance company is considered to be a breach of contract case, which means that the statute of limitation is 4 years. And it is not 4 years from the date of the injury, but 4 years from the date your insurance company wrongfully denied your claim. (read a case Taub v. Houston Pipeline Co., 75 S.W.3d 606, 618-19 (Tex.App.—Texarkana 2002, pet. denied). The cause of action in a breach of contract accrues when the contract is breached, or when the claimant has notice of facts sufficient to place him or her on notice of the breach.
Even though the statute of limitations is 4 years for a UIM claim, it is usually better to file suit within 2 years because, many times, you will have an argument that the insurance company acted in bad faith or violated the Texas Deceptive Trade Practices Act, which both have a 2-year statute of limitations. Thus, if you rely on the 4-year statute of limitations, you still will have your breach of contract case against your car insurance company, but you may not be able to assert some of the other theories that could increase the value of your case.