Very important for MSN/Live. Somewhat important for Yahoo. Less important for Google. (Vague I know, but nobody can give you percentages) On page optimization helps topical relevance if you build a tiered site with keyword focused pages. Links to a page with "widgets" as anchor text is better when the page title and headings include widgets in them. Content keyword density is not a focal point for any of the search engines (except maybe Yahoo). I don't believe in calculating keyword density and changing content to accommodate it.
It is important..but dont give that much importance to them as theere are more important things..like tha backlinks, age of backlinks, Pr of backlinks, traffic and so on
Agree with supercops comment. Google is big on backlinks. The age of your domain and the age of your backlinks carries a lot of weight with Google on competitive keywords, not as much a big deal on long tail keywords. Google also seems to really consider you more relevant if you receive, and give, links to market leaders in your niche, and get links from the same places they do, selectively. By selectively, I mean that you will find many high ranking sites that get unrelated, non-topical links. They will also have links on pages with 500 links on them. They will also get links that include spammy domains (viagra/casinos/porn) on the page. I don't really chase those links. But you do want to look at where the ranking domains are getting their links for sure. Google likes fresh content, and a lot of content. If you have the ability to generate a lot of quality content then that will help out too.
You need to find the best targeted keywords relevant to your business. So "on page SEO" is very important. You want the keyword of your content recognized by Google as important and by the readers.
I think to have a very successful website, having both Internal SEO and External SEO is the best option. Some search engines like Yahoo and MSN pay attention to the content more, whereas Google is very much based on backward links. A site can succeed with one or the other, but as more and more competetors are putting money into optimisation and getting their sites well optimised, the wise thing would be to work with both internal and external SEO. External SEO is a constant link building scheme, and needs to be started ASAP. This gives your site a good basis and if you are ahead of your competitors now with this, chances are you will be even further ahead if you put the effort into it now.
i still believe that "content is a king" from rich content comes your keywords and through keywords comes the crawlers.