I would/do use it whenever I have to split any string and I expect more than two pieces. If I just have two pieces, I'll use IndexOf. I like the readability of the named groups in a regular expresion.
I also use it for validation of strings, if needed. My company uses it this way and I love it! There's custom code to do the actual validation, but to define a new "datatype" for a DataSet column we use regular expressions (when needed of course).
-nerseus