Why do some cuts leave scars, while others do not?
This depends on a number of factors. Here are the first two that come to mind:

1) Is the cut deep enough to reach the dermis (this is the layer below the epidermis) where scar tissue will form?

2) What is your general state of health, and was there an infection at the site of the cut, which would have altered the normal healing process. 

Basically, not all cuts are created equal, especially if some are deeper than others and become infected. 

This article studied scratch depth
http://www.ncbi.nlm.nih.gov/pubmed/17440346