Mine is Quantum Leap. It ran from the late '80s and early '90s, and it was about Dr. Sam Beckett, who 'leaped' into different peoples' lives to fix mistakes in their own time. He was assisted throughout his missions by his friend Al Calavicci, who was also a hologram that only Sam could see and hear.
I've always had an interest in time travel as a concept, and this show handled it quite well, I feel. The writers of QL also stuck to a rule that Sam could only leap within his own lifetime (from the early '50s to roughly the early '80s). This was broken in a few episodes, but for the most part it was consistently followed throughout its 5 seasons.
Well, enough about my favourite show. What's your favourite show that is over 20 years old? Why do you like it? What's your favourite episode?