It really depends on the state, dealer etc.
I used to test drive cars when I was 19. Most places you'll go will want you to be 21 for insurance reasons but occasionally a dealer will waive it if they think you're serious about purchasing a vehicle or the dealer is desperate for a sale.
1995 M3 Coupe - HPDE/Track Prepped - For Sale
1997 M3 Coupe - BMWCCA I-Prepared Race Car
2011 335d - Das Uber Commuter (35.1MPG Avg)