So, there's apparently no hope for me, the hapless Windows 7 user. But if you're using Windows 2000, XP or 2003 (and only if you're using Windows 2000, XP or 2003), you're in luck!
This MSDN document contains instructions on how to disable auto-play on individual drive letters.
Basically, you start by taking the drive letters you want to disable. For me it was E, F, and G.
This is a binary number. Change the digits under the drive letters you want to disable auto play on to 1. Like this:
Ignore all the leading zeroes. Now I have
Convert it to hex with the Windows calculator or whatever.
Now open the start menu, type
regedit and go here:
Go to the menu and select Edit > New > DWORD (32-bit) value.
NoDriveAutoRun. Now, type in the number you just figured out. Close regedit. Magic! Rebooting may be required for the change to take effect.