Question: This is something I always wondered about but never really asked.
Say I have a rectangle box, image or other element in photoshop, when I make the desired element active and I check the info panel, The width / height never shows up - Should it?

Answer: 
When you make a selection, the 'Info' panel should show the width (W:) and height (H:) of the selection. It has to be the active selection, though.

*Note: The active selection "marching ants" don't show up in the screen capture.*

![alt text](https://i.stack.imgur.com/3SxFN.png)
Press 'Command-T' to transform the current layer. That will also show it's width and height in the info panel, as per Robert's answer (but more convenient).