Is it possible to make path to /%? My question: Is it possible to make path to /% ?

I have path that goes categories/% and that works when I type categories/hats it returns me category hat with all product it's taged with. 

I would like to be able to type url/hats and to have above explained functionality.

Is this possible and what do i change in view it is not possible to make path just /% ?
You can do that quite easily with the Views module and contextual filters.

The one thing that I don't suggest doing is using Taxonomy.  I don't like using taxonomy because besides it being a non-indexed list of vocabulary, it allows for too much variance.  For instance in taxonomy:

"hat" != "Hat" != "hAt" 


So, if you tagged one page as "hat" and the other "Hat", you would have to search for both term to get the content to display.

It much better to use the existing functionality of Content Types to create your "taxonomy."  Coupled with Views, Entity Reference, and Path Auto, you can do exactly what you are looking to do with a minimum of additional modules and "no taxonomy." 

I would definitely suggest taking a look at the Relativity Data Model put out by Jay Epstien.   

The Florida Drupal Camp website was redesigned with this model.  The most important thing to notice is the speed at which things load.  

I have also been using it quite extensively and can tell you that excluding content, my site is less than 5K in size; that's about the size of an iPhone app.  This is accomplished mostly due to the fact I am running less than 20 modules total.