I'm moving from one computer to another, and I'm wondering where my pilot and save data is stored so I can transfer that over.

If you're using DOSBox they're most likely in the main program folder. Where the executable is.

Oops, forgot these boards were Descent in general. I'm playing Descent 3, and there appear to be no save files in the program folder (they are definitely accessible through the game).

EDIT: I found them! They were in ~\AppData\Local\VirtualStore\Program Files (x86)\GOG.com\Descent 3\savegame rather than C:\Program Files...etc.

When you install a game to the Program Files folder in Vista or Win 7, 95% of the time the save files (and usually a config file or two) will be in the AppData folder, usually in the Local\VirtualStore subfolder. So be prepared to go digging through the AppData stuff if you install things there. Alternatively, you could install stuff to C:\Games\ or C:\Descent 3\ or whatever, which can prevent a variety of other issues as well. For instance, Fallout 3 gets weird glitches if it's installed to Program Files.