I was passenger in a car driven by a drunk driver and I was injured when they crashed. Can I sue them?

The short answer of that is “yes.”

Every operator of a motor vehicle, whether they’re sober or drunk, has an obligation to maintain their car in a safe condition and not cause crashes. If you’re a passenger in that car and the driver made a mistake, ran a red light or was drunk, or both, yes, you can file a claim against that driver.