I have been programming in Java since 2004, mostly enterprise and web applications. But I have never used short or byte, other than a toy program just to know
I found I was using byte variables when doing some low-level image processing. The .Net GDI+ draw routines were really slow so I hand-rolled my own.
Most times, though, I stick with signed integers unless I am forced to use something larger, given the problem constraints. Any sort of physics modeling I do usually requires floats or doubles, even if I don't need the precision.