Big emotional payoffs aren't new to Doctor Who, of course - ever since it's 2005 relaunch it's had a strong sense of it's characters and trying to keep everything rooted in something emotionally "real" even when you're flying through space and time in a little blue box. But even before that it made some decent stabs at that sort of connection and even as a kid I recall being affected by Peter Davidson sacrifice at the end of "The Caves of Androzani", for example. But as a general rule what I remember is stories, not emotions.
The shows I'm most attached to from the 90s are shows that ran with good, on-going stories. Babylon 5 was all about it's arc plot, Deep Space Nine went the same way. Buffy the Vampire Slayer really started to struggle when it went for (clumsy) emotionally story arcs late in it's run for all that it's success is rooted in strong characterisation. All of these shows did do emotionally based episodes, and all of them put out some good ones, but they're not the episodes I remember the show for.
But my two favorite shows of the last few years - Lost and Battlestar Galactica - take a different approach, especially with their finales. Both have huge and complex mythologies that almost certainly got away from their creators at some point, and both focused on getting emotional resolution for their characters instead of trying to wrap up everything neatly. I really couldn't care less about caves with glowing light in them, or mysterious smoke monsters on The Island, but I grinned like a loon when they bloody airliner finally got off the ground, or some of the long-parted couples reunited in the parallel universe. Its a different sort of resolution that we are led to expect from these sorts of shows but for me, it delivers.
The moment Fringe came together for me was the moment the truth about Peter was revealed, and it had nothing to do with parallel realities and strange conspiracies but everything to do with a father who couldn't bear to lose his son.
This may of course be me - I am now a husband and a father and I suspect that by pushable buttons are different to the version of me that was watching Babylon 5 back in the day. But I also think that genre shows spent a lot of time developing their heads back in the 1990s, bringing big plot arcs, series bibles, and the like to the forefront and making them something we expect now. We're not impressed by it any more, simply because it's the price of entry now. But engaging our hearts, thats still pretty new.