It is never a good idea to drive without insurance. If you get into an accident that is your fault, you will likely face criminal and administrative fines, in addition to whatever costs associated with accidents for which you are deemed responsible.
The extent to which you are on the hook differs depending on the state.
In a “no-fault” state the other driver will, at least in theory, have his or her bills that result from the crash covered by their own insurance company, but only up to a certain amount. If costs exceed the amount the other driver’s policy covers, they may try and sue you. If you lose, you will responsible to pay the costs out of your own pocket.
In “fault” states, it is likely the other driver will sue you for costs associated with the crash. Some insurance policies have an uninsured motorist claim, which covers the cost of an accident when a driver gets into an accident with a motorist who doesn’t have insurance. However, once the insurance company resolves the claim, it may try and sue you to recoup the costs.