The major reason is that I don't really like the gear game. I don't like making Best-In-Slot lists, or debating exactly what gear I need off what bosses. I just run stuff, and if something drops, I take it if it is better than what I have. My gear tends to evolve organically.
A good attunement chain or questline gives me a reason to run dungeons. It's something that I'm working towards, rather than my average gear ilevel hitting some minimum threshold. I do like beating every boss once, but after that you're just doing dungeons to prep for the next boss, or for social reasons.
I like having that extra goal to work towards.
Another element that was kind of similar were the old 8-piece class sets. I like collecting class sets, and don't mind running dungeons multiple times to get the set. I'm not really sure why this is different from running dungeons to get a pre-defined Best-In-Slot set, but it just is. Perhaps its the difference between making your character more powerful versus just collecting sets.
It just seems like in Wrath and Cataclysm, you ran 5-mans in order to make your character more powerful, so you could tackle raids. While in Vanilla and TBC, making your character more powerful was a secondary goal. You ran 5-mans to work on your attunements, or to collect your class set, or work on your class mount quest. And almost as a side-effect, your character got more powerful.