Hoff to Cowell: Your Girlfriend Gave Me Rugburn

David Hasselhoff has now done something Simon Cowell may never do -- propose to Terri Seymour!

For some unknown reason, the Hoff got down on one knee for Cowell's main squeeze outside of a marriage chapel at Planet Hollywood in Las Vegas -- and wooed her with the impossibly awkward line, "I'm single, and I don't like being alone."

Earlier that evening, Hoff took the stage at club Prive and performed one of his "hits" for the half-his-age, non-German crowd -- and they actually seemed to enjoy it! The world will now end in 5, 4, 3 ...