"Basic requirements" could mean more than just the state-required minimums for liability insurance (coverage that pays for damages to others and their property if you are found to be at-fault for an accident). Those minimums do vary by state, and you can find yours at your state's Department of Insurance web site, or by contacting an independent insurance agent. There's also a handy state-by-state list here. I'd use the state's website to get the most up-to-date information, though.
Other coverage that might be considered "basic" include:
collision coverage - which pays for damages to your own car in the case of a collision)
'other-than-collision' coverage - also called comprehensive coverage, and covers damages to your vehicle from, you guessed it, things that aren't collisions, e.g. fire, theft, vandalism, falling objects, explosion, earthquake, flood, and civil unrest
uninsured/underinsured motorist protection - coverage that pays for damages when the other party is found to be at-fault, but has no liability coverage to pay your damages, or if the accident is casued by an unknown hit-and-run motorist. Underinsured motorist coverage kicks in if the other party HAS insurance, but it is insufficient to cover your damages.
medical payments coverage - coverage for medical bills for the insured and others that is available regardless of where the liability for the accident lies
There's some nuance to some of the above coverages (hitting an animal isn't typically treated as a collision, for example), but the above summarizes the basics. By law, you'll need the state's minimum liability protection. I always recommend that clients look into at least the above coverages as well. After all, if you're in an accident, it's probably not going to be your fault, anyway, right? :)