for racing here we are not allowed to run less than 6mm. which is about 1/4 inch, i think you can go as thin as 3/16 but then you should propably run two vertican supports (nascar style) to prevent it wobling, but a windscreen with high curvature will be less prone to wobble than a flatter one. and when it gets scratched (which happens fast) you can buff it with a paint buffing and polishing compound, just dont use the coarse stuff.
Had a piece of 3/8 for a temporary windshield on my T-bucket for last summer.(Got it for free, so even if it was too thick, it was great!) Worked fine, but scratching & cleaning are a problem. Found out that Pledge furniture polish sprayed on and wiped off with a new soft cloth was the best. If you're thniking about running it on the street, be forewarned it ain't legal most places.
Not that being legal has ever stopped most of us!!