There are far more accurate (better) ways for search engines to determine true relevance than keyword density, and each search engine has its own means and methods to rank sites for a particular keyword or phrase. Search engines consider usage data, anchor text of inbound links, site/domain age, and general authority (all of which have been discussed here at search engine optimization software tools they use, have not. Where keyword density tools fall short is their ability to provide meaningful assessment and objective insights into ranking improvements. But keyword density tools are meaningful when used in conjunction with the right tactic. The "right" tactic in this case is to reduce on-page irrelevance and to boost relevance.
The semantic algorithms of popular search engines typically look at supporting vocabulary when determining the relevancy of a page. The question to ask yourself is simple: If you removed the keyword phrase being targeted from your page, would it be very easy to rank for that term? If search engines can still determine what your page is about with the remaining/supporting text, then the answer is a definitive Yes. Let's look at a few popular keyword density analyzer tools to see this in action.
Dave Naylor's Keyword Density Tool provides metrics about the content and even some technical information about a website. The tool provides several data points which are useful when trying to get a big-picture view of why competitors are outranking your site. For example, you might notice that a website with which you are competing has a higher keyword density in its title or page headings than you do. Naylor's tool provides a quick overview of this very important information.
Should you want to dig deeper into the relevancy of keywords and pages on your own site (or that of your competitors), then check out Ranks.nl's Keyword Density and Prominence Analyzer. The tool provides a "Ranks Wizard" metric that is helpful in identifying the non-primary keywords on a page to support the search engines in their quest to relate/associate keywords and phrases and as you optimize for the long tail.
These tools and many others are useful in determining how relevant a page is to a specific keyword and in gaining the perspective of a search engine crawler, but they are also useful in finding and minimizing irrelevance. As search engines continue to evolve their algorithms, rest assured that keyword density remains a good initial measure of future performance (but only if you know how to use it). Does keyword density carry as much "weight" as it did before? Not by a long shot, but when you know how to use it correctly and to your advantage, your site's ranking will be that much better. Instead of chasing some specific keyword density percentage, use density as a measuring stick to reassuring yourself that you are doing all you can to convey to search engines that the page you are optimizing is indeed relevant.