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: 
If you activate the transform tool on a layer (`CMD`+`T` or `CTRL`+`T`), you'll see that in the top panel, the X/Y position is shown along-side the size, angle, etc. 

The size is in *Percent* by default, but right-clicking the field gives you a selection of measurements to pick from, *Pixels*, in this case.

![enter image description here](https://i.stack.imgur.com/M5I99.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).