I think the courts have looked at sobriety checkpoints and decided that it enhances public safety and therefore is allowed.
Other than that... stopping for license checks, or vehicle safety inspections, etc. are a violation of the 4th Amendment, IMHO.
As for driving being a "right". California considers driving a privilege. AFAIK, the DMV can revoke a license at their discretion, without a court decision, and no appeal. In the cases of DUI, they will revoke a license even before the court date.