What are basic car insurance requirements?

Basic car insurance requirements vary by state. Most states require bodily injury and property damage liability. Liability limits are also different from one state to another. Some states also require uninsured motorist coverage and/or personal injury protection.

"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?  :)

The basic car insurance requirements are different in each state.

This depends on where you live, as states have different laws. In most cases, you either need to have an insurance policy that includes liability coverage or you have to prove financial ability to pay for damages should someone be injured as the result of your actions. I suggest you look at the website for your state's department of insurance to determine the minimum requirements for this liability coverage.