The answer to this question depends on what you mean by "driving without a license."
First, let's say you actually have a valid driver's license--but you forget it at home and end up getting stopped by a CHP or other law enforcement officer. This actually is a crime -- California Vehicle Code 12951 VC failure to display a license.
However, failing to show a driver's license, where you simply forgot your license at home, is only a California infraction. It carries a maximum potential fine of two hundred fifty dollars ($250). Not only that, but if you can show the court that you did have a valid license at the time of your arrest, then in most cases you can get the charge dismissed.
Second, let's say you were caught driving at a time when you actually did not have a valid driver's license. Maybe you'd never obtained a license, or maybe your license expired and you did not get around to renewing it.
In that case, you can be charged with Vehicle Code 12500 VC driving without a license. This crime in most circumstances is a California misdemeanor. It carries up to six (6) months in county jail and/or a fine of up to one thousand dollars ($1,000).
Finally, let's say you drive without a valid license--and the reason is that your license was suspended or revoked for a particular reason (like a DUI conviction). This is the crime of Vehicle Code 14601 VC driving on a suspended license.
Driving on a suspended or revoked license is a misdemeanor. But the penalty scheme is complicated and depends on why your license was suspended in the first place. More details can be found in our page on penalties, punishment and sentencing for driving on a suspended license.
And if your license was suspended for a DUI conviction, there is a good chance that a driving on a suspended license charge will result in a probation violation in your DUI case. (See our related article, California laws for driving without a license versus driving without a license in possession.)