What theme are you using? Have you created a custom menu per –
http://codex.wordpress.org/WordPress_Menu_User_Guide
Have you set up categories under the categories screen – you have to do that first:
http://codex.wordpress.org/Posts_Categories_Screen
I am using a custom paid theme right now, but even if I switch to one of the default themes, I still only have the one option for standard pages.
I currently have about 15 categories on the categories screen, and almost 60 tags, but no box on the menu screen for either.
Aha! I found it – apparently I have to allow categories and tags in the screen options pulldown! Thanks for the links, found it there.
Under the Pages box, do you see other headers for Links, Categories, Format?
If not, have you tried deactivating all plugins and switching to the default theme?
Are you using WP3.6.1?