Incomplete Required Fields

Has anyone else noticed a influx of records entering their system through forms with required fields incomplete? We're having large discussions around people disabling their javascript to bypass the requirements.

We have already implemented a "no javascript" message to warn them they will lose the full functionality of the page but still allow capture of whatever information they may chose to populate. We are also investigating other possible  avenues of this data entering the system outside of javascript disablement. 

If anyone has suggestions on how to address this issue would love to hear from you.