I always put the keywords 2-3 times per 400 words and it works fine for me. More important is using lots of synonyms of your keywords in there to make the whole article relevant.
You can place your keyword once every 100 words. This is the general rule I always follow. I always make sure to place my targeted keywords in the title of a post, in the first paragraph, and in the last paragraph.
Id agree with StevieP, i think the longest article ive written was approx 500 words and i had no more than 2 links in it. Most article directories allow you to enter an author box and sometimes let you put links here as well.
There is no optimum keyword density. There are examples of pages that rank well with all kinds of denisty values.
dear all the default keyword density for all search engines is 2% and not more then that. But then it again depends on the nature of the articles it has been written for and how well is the article written. some articles and topics are such that you don't have any other options then repeating the keywords as there would be natural re appearance of the same. so all that matters is not the density of the keywords but its the content of the article and its uniqueness and it should be written for humans and not search engines. if you take care of this things you don't need to actually worry about the density of the keywords.