Probably the most bizarre educational bit I got from D&D was that I used to know the Dewey Decimal System well enough that I didn't use the card catalog at my high school library -- it was faster for me to walk to the right section and actually look at the titles than to flip through a bunch of index cards. I freaked out most of my friends at least once. But, that's also the best illustration of just exactly how much stuff I learned from D&D.
More specifically:
Folklore, Mythology, and Comparitive Religion
Kind of a cornerstone of D&D. What are the oddball beliefs of every backwater village? How do different beliefs interact? What causes a group to shift from one belief system to another?
History and Biographies
This started off with an attempt at Medieval verisimillitude, but history is such a big, fluid topic, that you always need to find out the rest of the story. I'm not really a history buff, but I do know more than the average bear.
Geography, Cartography, Meteorology, and Geology
Maps, maps, maps. Every game world needs some. If you get really into things, you can even learn a bit about plate tectonics to craft better a better map. Looking at the real world helps here, too. Plus, it's awfully hard to study history and not get a better feel for geography.
Chemistry, Physics, and Metalurgy
Someone will inevitably ask, "just exactly how hot is a fireball and what does it melt?" After that, you pretty much have to learn to use a Handbook of Chemistry and Physics. Not to mention asking why there isn't any gunpowder (or is there?) and other questions that boil down to "How real is your fantasy?"
Astronomy and Astrology
A little bit from the geography category and a little bit from the physics category. Adding constellations to your homebrew world is pretty cool.
Statistics
If you're going to tinker with rules that involve dice, it's a real good idea to know what impact your tinkering has.
Art
Two reasons for this. First, art is very evocative in a setting and it's culturally important (see History). Second, you can't study art without wanting to try it some -- I do passibly well with clay, pen and ink, charcoal, and pastels, though I'm way out of practice anymore.
Language
That's how Tolkien got started, and I eventually moved that direction. Some of it was required by history readings. Some by science readings. Some in trying to create my own languages. Plus, learning accents and a few words really helps bring NPCs to life.
Biology and Ecology
Same as most of the other sciences. If nothing else, it's nice to be able to have intelligent placement of wildlife. I didn't learn a lot, compared to some of the other areas, but I seem to have retained more info than most adults.
Politics and Philosophy
It's great to set up imaginary states and figure out how they interact with one-another. Plus, there were so many cool tables in the DMG. I eventually graduated with a Political Science and Philosophy degree, so it's hard for me to say how much D&D pushed me and how much I pushed it on this topic.
Computers
I can't even count the number of times I've started on a character generation/management tool. My first was on the C64 and I'm thinking about starting another one in .NET. When I discover that, while I like studying politics I don't have the stomach to play the game, I had no problem transitioning to programming computers because of all the utilities I'd built over the years. In fact, I seem to be at least on par with people my age who actually did the CS degree.
