Here's what I did for my band last year:
I decided to redesign our logo because our sound got much heavier and even more melodic. I felt our original logo (below) didn't show who we were anymore.
All I did to design the new one is look at bands I know we are similar to as well as other bands' logos that I really like. I took my favorite aspects of each and tried to combine them all into one.
To me, it was really important that the logo be easy to read and have lots of rough edges.
I really like the end result. It made for really easy application to our website and merch (shirts, etc.).
Music washes from the soul the dust of everyday life.