In Texas you do not need a license to carry a handgun in your car provided you follow some pretty basic rules.
First, the weapon must be concealed. Many citizens choose to conceal their handgun in a glove box, trunk or inside of a bag. If you fail to keep the weapon concealed you could be arrested and charged with an offense.
Second, you cannot commit a law violation while you are in possession of the handgun. A good example would be if a person was DWI with a handgun in the car. This wold make the possession of the handgun now ILLEGAL. What would normally be innocent behavior will become criminal because of the DWI.
Finally, some persons are prohibited by law from being in possession of a handgun. This would include convicted felons or members of a criminal street gang. A person in one of these categories would be in violation of the law if they possessed a handgun in their vehicle even if it was concealed.