Almost all states as well as District of Columbia have compulsory insurance law as it requires auto owners to have liability insurance before they can legally drive. Unfortunately the laws are not that perfect due to several reasons:
Compensation for the victims must come from traditional legal channels and can be delayed by the overburdened legal system.
These laws do not guarantee that the innocent victims will be compensated; you may be injured by a hit-and-run driver, you may be injured by a an out-of-state driver without insurance, you may be injured by a driver of a stolen car, etc.
Required limits are relatively low for bodily injury claim and property damage claim.