I was just browsing my passport and saw that I have a stamp from my previous Visa application for the USA. It's dated June 17, 1997. It has no status stamp (approved/rejected), but I think it was denied. Will this affect my application for a UK Visa?
yes, it was denied coz no visa appeared on your passport. If you will apply for a fiancee/spouse visa it will not affect your application. As long as you can satisfy the ECO of the ff:financial, accommodation and your relationship.