PROPER keyword density does indeed make a difference in the search results. That is how Google and other search engines rank the content on a web page for placement in organic search results. While recent algorithmic changes made by Google, such as Penguin, target spammy and duplicate content, legitimate keyword placement throughout a webpage does affect average placement in the search results.
As search engine spiders crawl a website, the content on each web page is analyzed and categorized according to common threads and similarities. The words used most frequently are those the spider attaches the most significance to when the content gets indexed, the reason being that they figure if something is used a lot on a web page, it is relevant to the overall message of that page. Have you noticed how when you do a search in Google, the results will have your search terms emboldened? What you see is the actual content on the page. Good keyword density is a major factor in how well a particular web page is ranked in the search results. There are also other key factors, like internal and external links to your site, the age of the site, and the uniqueness of your content.
Regarding my use of the term "proper", what I mean is this: there is a common misconception that if you simply repeat a particular keyword a bunch of times on a page, you'll rank higher for that word. At one time, this may have been true, but as more and more redundant and spam content was added to web pages, the search engines set safeguards in place to penalize such tactics. The key to effective keyword density is to use terms and phrases that are relevant throughout the page in a way that doesn't seem contrived or spammy. Use important terms more frequently, but in a way that flows naturally with the content of the page. Use different ways of saying the same thing. For instance, on a web page about mylar, you could use "laminated mylar", "alluminized mylar", "polyethelyne terephthalate", "biaxially oriented polyethylene terephthalate", "BoPET", and a dozen or so other terms and phrases that all refer to the same substance: mylar. Using different ways to say the same thing keeps you from seeming redundant or spammy.