How can I change my default My Music, My Video, My Picture and other Folders without installing a program to do it?

If you want to define different folders for My Music, My Video, My Pictures and so on, you have to modify some values in the registry.
http://www.infopackets.com/channels/en/windows/gazette/2004/20040415_change_my_documents_music_pictures_path.htm

Another way I could think of would be to create a shorcut to a folder inside one of those folders you want to redirect from.

For example:
You want to save to D:\Backup\My backup\Multimedia\Photos\Family photos
But you want quick access to it via My Pictures folder.

You can create a shortcut to the folder to D: drive folder inside My Picture folder.
When you want to save a picture to that folder in D: drive, you then can double click on the shortcut to D: drive folder from Save As dialog, inside the My Pictures folder. You will then arrive in the D: drive's folder.

This is quite clean as you won't have to mess with the registry, and when you don't want to do it anymore, you can just delete the shortcut from My Pictures (or similar) folder.

Hope this is what you want to achieve? Since this is not shortcut on Desktop. When you open some program that refers directly to My Pictures in it's Save As / Save dialog, you can just double click on it.

You can change the default IE download folder... not really the same, I know...
Start->Run->Regedit
Navigate to HKCU\Software\Microsoft\Internet Explorer\Main
"Save Directory "

Not sure why you don't do like I have done, and everyone I know has done. Just create a folder on that hard drive, and if you want a shortcut, make a shortcut to that folder?

"because I like when programs open right up to the right folder (Adobe Photoshop to My Pictures, Music programs to My Music, Video to my Video, etc.....) "

Each and EVERY program is editable to what it opens to... you should look at changing optional application software before modifying the OS.

"Plus some of the features of Windows XP that just make it more easy to navigate."

LIKE WHAT? Anything you mention, like start menu, etc, you can change to your folders on the other hard drives...

You don't want another program, but yet you want to do something that MS doesn't want you to do. I mean, in the link that Allocator gave you it says, "Shell folders may be moved in a [number of ways, including TweakUI for XP, or by implementing a registry hack].""

Without using another program, you should do this:
Click Start -> Run, and type in "regedit"
 
HKEY_CURRENT_USER \ Software \ Microsoft \ Windows \ CurrentVersion \ Explorer \ Shell Folders.
 
Right click on the folders you want to change and select Modify.
 
Change the path of your folder to the new path (example: d:\my music).
 
Reboot your computer.