It's one of those things I've loved since vanilla. My first character was a druid, and I remember after finishing the agonizingly long chain to obtain aquatic form, I decided to put a hold on questing and instead swim around the entirety of Kalimdor, from Darkshore to Silithus and back around. I died a lot. But the journey was incredibly fun, and I got to see areas I never would have encountered in the normal span of questing, and familiarize myself with just how big the world actually was.
It's something I do every expansion -- swim, climb, crawl, jump, and poke around every nook and cranny of the map until I'm satisfied I've seen absolutely everything there is to see. After all, someone out there at Blizzard went to all the trouble of building these far-flung areas and caverns. Of course I'm going to give them a look. But what about you guys? Do you spend any time in the game just running around and exploring the world? Have you ever had a strange trip under the map? What was the coolest hidden away area you've ever seen? How much do you explore?