It depends on the claim. Being in a crash that was not your fault, and recovering from the at-fault driver's insurer, is treated differently from causing an accident yourself. You should not be penalized because someone else hit you, though insurance practices do vary.
Using your own coverage — like uninsured motorist or collision after a hit-and-run — is coverage you already paid for, and it exists for exactly these situations. Worrying about rates should not stop you from using benefits you are entitled to, though it is fair to ask how a particular claim may be treated.
The bigger risk is often not making a claim at all and absorbing costs that someone else should cover. If you are unsure, a free review can help you understand your options before you decide.