If you do like dungeons (or at least like them as much as other adventure locations), what do you like about them? How do you approach them as a player?
As a player, I usually approach them by wading in and exploring until there's something to either beat up, loot, or both. Then that thing gets beaten up, looted, or both. Lather rinse repeat until we've done whatever bigger task we went there to do, then go home and divide the spoils.

I like dungeons because while I-as-me can go out and explore some woods etc. anytime I want, I can't go exploring dungeons - they add to the fantasy element. And the whole exploring piece is important to me.
If you're a DM, what kind of resources do you use to help you design and run them effectively?
I'm not sure I design them "effectively", if by that you mean the least bit efficiently. It's usually either pretty labour-intensive (if I'm trying to doll it up so someone else could run it) or pretty slap-dash with lots of notes and maps on scraps of paper.
Running them is easy, though, in that the whole environment is (in theory!) laid out in reasonable detail ahead of time meaning I rarely if ever have to do any on-the-fly creation. All I have to do is narrate and referee.
Contrast this with an outdoor or city adventure, where it's kind of impossible to detail everything ahead of time and thus a lot of stuff gets made up on the fly...which would be fine except my at-table note-taking is atrocious and I'll sometimes forget things 5 minutes after I've said them (I blame beer). I can run these, but they're way more of a headache unless I want to railroad the party, which I'd prefer not to do.
(I'm making this a D&D 5e thread because that is the most recent and arguably popular version of the game. If you're going to talk about other editions or even other games, please say so explicitly so as to mitigate misunderstandings as to rules or the like.)
Everything I say above is, I think, edition-agnostic; though I'm coming from a very-much-pre-5e point of view.