I think there are some good points here, but I want to warn that it really depends. There are sites with 250-word pages that do well, if that content is unique and isn't buried in ads, etc. If you have 1,000 words but it's all syndicated from other sites and jammed with ads, you could have Panda breathing down your neck.
I would generally not worry about keyword density. Write natural copy, with solid topic focus, and your keywords will organically end up represented in various forms. Google is a lot more sophisticated than just counting keywords or density these days, and trying to engineer the perfect number is more likely to harm you than help (as others mentioned). Plus, you can drive yourself crazy for something that will ultimately have a very small impact.
What I think is a lot more important is your overall keyword strategy. Instead of worrying about how many times a keyword is on a page, focus on the structure of your site. Which pages target which keywords? Are there important variants that need their own content (and can you create unique content for them)? Are you spread too thin. I see many more problems caused by bad keyword strategy ACROSS sites than within any one page.
