I can't find my iPhone on my computer
I usually sync my iPhone with my Mac at home so testing it on my work PC does not give the option to mount the phone to sync music, pictures, etc. That said...

If I recall correctly you have to download and set up iTunes to sync with the PC in question. Then iTunes will mount (at least) the Pictures folder and allow you to copy things off of it manually if you so choose. (again going from memory, I may have a detail or two incorrect)

If your goal is to use your iPhone as an external storage device or to explore the contents of the phone then you will need a 3rd-party application like iPhone Explorer installed on your PC to have access to the iPhone's file system and to be able to copy files back and forth at will.

I have always wanted to be able to just plug an iPhone in and use some of the available storage as you would a thumb drive. But Apple has chosen to not implement that functionality out of the box for some reason.