I watched re-runs of this as a kid - it started in 1982, so it's 31 years old now! Really enjoyed it back then although I'm not sure if it holds up today. Here's the premise courtesy of wikipedia:
Remington Steele's premise is that Laura Holt, a licensed private detective played by Stephanie Zimbalist, opened a detective agency under her own name but found that potential clients refused to hire a woman, however qualified. To solve the problem, Laura invents a fictitious male superior whom she names Remington Steele. Through a series of events that unfold in the first episode, "License to Steele", Pierce Brosnan's character, a former thief and con man whose real name is never revealed, assumes the identity of Remington Steele. Behind the scenes, Laura remains firmly in charge.