From what I've been told by HR folks—and from my time as an office administrator who got to handle the HR, too—bullet points are a good idea. White space. Simplicity. Proper grammar and spelling. A name that's bigger than the rest of the text (indicating self-confidence).
The type of job you're applying for should affect your résumé. A graphic designer benefits from using those talents on the résumé, for example.
Personally, I open mine with an intro paragraph that expresses why you want to hire a weirdo who reads grammar handbooks for fun. Then I have a multi-columned bullet list with a brief listing of specific skills I have (like HTML, including HTML5).
Then I list my time as a freelancer with bullets giving examples of types of work I've done, then the full-time proofreader/copyeditor gig I had. I include a note that the list isn't comprehensive.
If the specific job I'm applying for is pertinent to another job I've held—like my time working for a market research company—I'll add that in.
But I designed my résumé to be easily skimmed, with plenty of white space. My résumé's affected by my experience as a web writer, and my experience proofreading newsletters in particular.
I also only bring it out when I'm specifically asked for one, which actually happens rarely. I'm currently rethinking that policy of only giving it when asked.
Whatever you do, when applying for a job, follow the directions. When I was responsible for a company's interviews and such, I quickly learned that anybody who couldn't follow directions while in the hiring process wouldn't follow directions as an employee, either.