Your running shoes are no good anymore far far before your soles get thin. The compressable materials in the sole lose their sponginess and take a set well before then. This leaves you with a shoe that does not provide you with proper stability and can set you up for injury.
You don't need to buy really expensive or fancy lookin' shoes to get good support. In fact, as a general rule of thumb, if the shoes have a whole lot of "whiz-bang", chances are they aren't very good running shoes (like a lot of nike's for instance)
I personally wear nothing but New Balance 991's. The advantage to buying New Balance is that their shoes come in widths, and are appropriately constructed for different foot types - flat, med arch, high arch. I have pretty flat feet so I get a shoe built for me.
There are plenty of other good running shoe brands. Good luck.