When I picked up playing on Kronos again after a break of several months, I dumped a whole bunch of group and dungeon quests from my quest log and vowed to myself that, in the future, I wouldn't allow them to bog me down. If I got them done, great, but I wasn't going to fret about it and if I outlevelled them before a good opportunity presented itself to complete them, I'd just throw them out without a second thought.
In terms of group quests, I've actually been pretty lucky since then - just as the ones in Stranglethorn Vale and Alterac Mountains were starting to build up and beginning to feel like a problem, I had a lucky day and got the whole lot of them done in two runs (one for each zone).
Also, I've been running dungeons again, mostly as a healer, even though I always feel a bit self-conscious wearing a dress as a paladin. I tend to not put my healing gear on until we're at the instance and I immediately take it off again as soon as we're done. Funnily enough, the one time I didn't do that and left it on for a bit while wandering around Ironforge clearing my bags, a dwarf paladin whispered me accusingly that paladins shouldn't wear dresses (it was clearly tongue-in-cheek but still telling)!
I'd kind of given up on the idea of actually tanking dungeons because it's just too annoying without a taunt, but ended up doing so for one SM Library/Armoury run anyway because everyone else in the group was several levels below me, which I figured would give me enough of a threat buffer. It did work out OK, though towards the end we had to replace one damage dealer and the new one was a shadow priest that was only one level below me or so... she had aggro pretty much until the end of the run.
The whole experience is also just so different from most dungeons in more modern MMOs. Syp posted about what he considers a good dungeon run yesterday, and Telwyn wrote a post in reply to offer a counter-point on the subject of why "should take 30 minutes or less" might not be a good requirement for an instance. I can actually enjoy a 30 minute dungeon run as well if everything else about it works for me, but there is a certain quality to these old-school, multiple-hour runs that seems to be missing from many newer games. Both the time and effort required and the rewards you get are just so much greater. There's the whole issue of having to manually assemble the group and getting everyone to the instance (the trip to Scarlet Monastery as an Alliance player is epic on its own), but then once inside you earn decent XP and the drops are just amazing. I'd completely forgotten how rare even greens used to be in Vanilla and I sell almost every single one I find on the auction house. My own paladin still has level twenty gear in several slots simply because I haven't had any appropriate drops or received useful quest rewards. So going to a place where you're pretty much guaranteed to see multiple blues or at least high quality greens drop is just exciting. It's pretty much comparable to pugging a (non raid finder) raid in a newer game, just with fewer people. I guess as someone who enjoys raiding to this day, it's not surprising that those old-school dungeons appeal to me as well - though I fully admit that I wouldn't want to be running them every day either as it would get quite exhausting.