My resumes in the past have followed the usual "standard" format that one usually finds in them, but with a couple of additons.
Make sure to include a section with your pilot qualifications with all of your certificates, ratings, and endorsements. It also doesn't hurt to state your type of medical. Then put in a breakdown of your flight times. Put down the important numbers like total, XC, night, ME, IFR, and any others you feel may give you an edge but don't go overboard. If you have time in a specific aircraft type that you feel may give your chances a boost, put that down as well. Only go this route if there is a particular airframe type that your potential employer uses and you have time in that type.
When you get down to the accomplishments or achievments section, put down any aviation related awards or recognitions or groups that you have. Examples would be Wings phases or any FAA aviation awards, and membership in EAA or AOPA.
Beyond that, make sure it's legible and not overly fancy and that you put a current contact info on it. Adding an email address to your contact information doesn't hurt a bit, but don't put down
[email protected] or anyting like that.