Can I upgrade from Mountain Lion To Mavericks without the app store? I don't want to create an App Store account because I don't like the idea of tying my computer with it.

Can I still upgrade from Mountain Lion to Mavericks for free from the Apple servers without an App Store account ?
In short: No, at least not yet.

What's wrong with creating an Apple ID? Your computer won't be tied with it as you can simply signout.
Even after installing Mavericks you have to set up an Apple ID, or skip the part afterwards.

You don't have to keep it connected.

Sidenote: You create an account here, but an Apple ID is one step too far?