For experimental purposes I just looked up the #1 spot for about 20 of my more recent target keywords ranging from 20-42 MoZ It was a wide range from about 0.8% and one oddity was 3.41%... CONCLUSION:Google DGAF so long as you say it enough times that it deems your article relevant to your target key term, and not so much that you're a spammer.
It's okay to keep density 0.5-2.5% as a rule of thumb, nothing more. Focus on the context and the idea behind the writing. I've seen highly ranked pages with lower than 0.5% density. Focus on the point and what you have to say. Though, it may depend on the locale you are targeting also. While Google ranking systems is quite advanced in English language, I've seen different results on Indonesia locale, where keyword stuffing sometimes works
I got a good kick out of reading all the responses but everyone was just guessing. Keyword density is real and does matter. What you have to understand is that the way you're looking at it is all wrong. You can't use 1 keyword density percentage for every page, it's ALWAYS on a page-by-page basis. What's the correct density on one article/topic is not necessary the same on the next. To KNOW what keyword density percentage Google is looking for, see what density percentage the 1st page ranking pages(for keywords) are using. These are the pages/density that Google is rewarding sites for and telling you they want/accept. If your density is way lower (under optimized), then you're not going to rank as well as you could. Have way higher (over optimized) density and you will not rank as well either. It all depends on the keywords/topic that's currently ranking 1st page. Yoast plugin gives a generic percentage for all keywords or a "rule of thumb".
You could stick to keyword density numbers threshold as suggested by many above but notice that search engines nowadays have become EXTREMELY intelligent. Its impossible to trick them nowadays as it was before. The best solution is that your content is: 1.SENSIBLE 2.ENGAGING 3.USES CORRECT GRAMMAR 4.NATURALLY SOUNDING 5.DELIVERS VALUE If you have all these five points fulfilled, search engine crawlers WILL notice your page and will rank it. I once happened to have written short one page article about content creation for newbies and NEVER did any keyword stuffing, link building, forum posting or any SEO tricks. Suddenly in few days I am contacted by email by a lady from USA telling me how good was the article and how much she liked it, to the extend that she was going to send me $100 as soon as she implements those tips and makes first money. So what happened?....Google just PLACED my tiny ugly article on the first page of Google by their own crawlers' decision! Just simply because they LIKED it. It was natural, succinct, interesting, valuable. It got independent clicks and likes from people worldwide, so Google immediately detected it and pushed it up without a single effort from me! The era when you were manipulating Google with keywords density is in the past. Nowadays Google knows what you think and what you are going to say and do even before you say or do something. So, take note.