Is a summary of your background something that really should go on your resume?

Absolutely. Professional Summary sells you! 

If you can make it a bulleted list, even better. Employers can scan it more quickly. Additionally, a rambling summary does you no good. Short, sweet and job specific focused if at all possible.  There is always a debate about what goes on the top of a resume, but I strongly advocate for a simple branding statement that describes the key attributes and nature of the person that would set him/her apart from the competition. Not a list of skills, past positions, or responsibilities.

 It is the place for a "meta" statement, to give everything else a context. For a mid-career individual, it should be 2-3 lines in length - maybe a bit more but not by much. A focused summary bringing value to the reader. Informing an employer, that you're a "jack-of-all-trades," no.  A well-written resume will "sell" rather than "tell." You attract attention of potential employers with your resume by emphasizing the benefits and value you have to offer and can bring to their organization. (TIP: It goes beyond a general summary and laundry list of core duties and responsibilities!)