The basic Car Insurance Requirements in Texas 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 20/40/15 (Bodily Injury and Property Damage)
20/40/15 Explained:

The first 20 represents $20,000, the maximum coverage for one person's injuries, $40,000 for the total coverage for all injuries sustained in one incident and last but not least $15,000 for the property damage maximum coverage amount.

Texas Car Insurance Laws:
Insurance proof is a requirement at registration and of course after an accident. The First Offense is a $175 - $350 fine.