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.
ZYXWVUTSRQPONMLKJIHGFEDCBA
00000000000000000000000000
This is a binary number. Change the digits under the drive letters you want to disable auto play on to 1. Like this:
ZYXWVUTSRQPONMLKJIHGFEDCBA
00000000000000000001110000
Ignore all the leading zeroes. Now I have
1110000
Convert it to hex with the Windows calculator or whatever.
70
Now open the start menu, type regedit and go here:
HKEY_CURRENT_USER
Software
Microsoft
Windows
CurrentVersion
Policies
Explorer
Go to the menu and select Edit > New > DWORD (32-bit) value.
Name it NoDriveAutoRun. Now, type in the number you just figured out. Close regedit. Magic! Rebooting may be required for the change to take effect.