West Wing, The Wire, and Boston Legal. Never considered watching them when they were on the air. Love all three now.
I didn’t watch Fringe till after the first season ended but caught up and am staying current with the new season.
Someone mentioned MASH didn’t really have the option to watch it when it was on the air but watch it regularly as reruns even if I’ve seen the episode its just a great show to have playing.
I was a massive fan of “Combat” (AKA: “Why Uncle Jerry is a bit crazy”) during its first run (I was a kid), but seeing it decades later I can see how good it really was.
When it was originally on I had no interest Millennium. Around 10 years later it’s playing on Chiller 7 days a week so I gave it a try and watched all three seasons. I really liked it and wish I would have given it a chance back then.
Me, too, but primarily because I wasn’t born yet while it was on the air. 
I only caught “Homicide: Life on the Street” when it went into reruns, and regret that I never saw the whole thing. It is on my list of series to get when I don’t have any other use for my money.
MAS*H and Frasier.
MAS*H was always a “dad show” when I was growing up–my dad loved it, which meant it was probably serious and didn’t have anything that would appeal to a kid. But I discovered it many years later and now I usually stop to watch it when I surf past an episode. Love it.
Frasier I didn’t watch because I can’t stand Cheers, and I thought it would just be more of the same. But then I caught an ep or two, realized it wasn’t Cheers 2.0 and that I really liked Frasier and Niles…from that point on it became one of my favorite comedies.
I didn’t see it until they were showing reruns on Lifetime in 1998. The earlier seasons were definitely much better. Up to season 5 is worth getting on DVD. It sort of goes downhill with the Luther Mahoney plotline, but still a pretty decent show.