It basically boils down to TV being a very different thing back then. There wasn't as much of an expectation of consistent forward character progression, episodes were designed to be standalone for easier syndication. Yeah, there was the occasional recurring villain — primarily Keigh Deigh as Wo Fat, who usually turned up in two-parters or season finales — but nothing approaching the long-running background plot arcs they've had going on the new show (i.e., the Shelburne arc in Season 2). For instance, in one episode, and I can't remember which season it's in, the woman Danny is engaged to is killed. We've never seen her before, and she's never referred to again. That sort of thing wouldn't fly with today's audience.
As for why it lasted so long? The same reason Law & Order
ran for 20 seasons and CSI
have been on 10+: people liked it and they kept watching.