I run old content almost constantly now, looking for that one perfect matching piece. I do old quests I missed when the Cata revamp came in. I've completed sets that I never managed to finish (that last two protector tokens from Heroic ICC that evaded me for the entire time the instance was current? I got them this month.) I even use Warforged Seals on bosses simply to get matching pieces for transmog sets. Transmog is a huge part of how I play now, and even why I play to some extent - if it weren't for transmog I probably wouldn't log on half as much as I do.
Not bad considering how much I hated the idea of transmog when it was floated over and over again over the course of the years I played before it existed.
It's humbling but also necessary sometimes to admit when you're wrong, and hoo boy, was I wrong about transmog. I used to argue that transmog would diminish the value of new art - instead, I often pick up pieces of gear in current raiding as much for their aesthetic appeal as anything else (I have the complete Warrior Tier 16, a set I don't even like, just because I want to be able to use the pieces for mix and match mogging) - indeed, my tendency to use our raid breaks in order to mog my gear often means I mog pieces I'm wearing to look like pieces I just got.
Similarly, I used to argue that with transmog, people would just mog to old tier sets (indeed, even Ghostcrawler mentioned on the WoW Insider show that's how the feature was originally conceived) but now I find myself mogging based on a common theme or color scheme or just on a whim. I have mogs that are based around a single piece of gear, or a color scheme, or just because I wanted to look as awful as possible.
I find that being free to customize my own look has me more invested in my play - there are days when I really feel like just putting on the Heroism pieces and using an old Blackrock Spire 2h weapon, and days when I'll tank a few dungeons just so I can put on a completely, wildly mismatched set of pieces that make my Icecrown Glacial Wall look absolutely ridiculous. I like that people don't know I'm overgearing the content just by looking at me anymore.
But most of all, I love being able to use my enormous weapon collection. Before transmog, I collected weapons just to have them - By the end of Wrath of the Lich King I had a large collection that was just gathering dust. I don't know and didn't then have every weapon I'd want, although I've gotten pretty close to every 2h weapon I would collect (I didn't really like any weapon in Throne of Thunder besides Uroe, for example, but I like most Siege weapons) - but there's just something so much fun about imagining my character going into this enormous weapon rack and just yanking out Ashkandi for the night, or deciding that it's more of an Armageddon raid.