The basic Car Insurance Requirements in New York are as follows:

Liability Insurance is a minimum requirement and a low cost car insurance option as long as the vehicle is not financed.

The liability Minimums are 25/50/10 (Bodily Injury and Property Damage)
25/50/10 Explained:

The first 25 represents $25,000, the maximum coverage for one person's injuries, $50,000 for the total coverage for all injuries sustained in one incident and last but not least $10,000 for the property damage maximum coverage amount.

New York Car Insurance Laws:
Insurance proof is a requirement at registration and of course after an accident. The First Offense penalty is a $150 - $1500 fine, maximum 15 days in jail.