When I first started out creating websites back in 2004, the search engines did not rely heavily on regularly updated content. The main attributes for success were an aged website with quality backlinks. That's why you would see one page websites from 1995 ranking in the top 10 for competitive keywords. Nowadays, the focus has shifted, and regularly updated content plays a major role.
So, how often should one update their content, and which pages should be updated?
The Homepage is without doubt the most important page in terms of SEO. It's the door to your website, and Google & co. place emphasis on this. That's why whenever you search for popular keywords, it's rare to see a sub-folder listed on the first couple of results pages. There is not a definitive answer on how often to update content, but at least once a week should be fly enough for the search engine spiders.
The regularity of fresh content can impact not only your SERPS, but your return visitors also. People love something fresh and new (ask Governments 
). Remember, the point of SEO is to increase your traffic, word-of-mouth / buzz can do this also.
If you are not particularly keen writer (like myself, evidenced with this blog) you can use a few tools to bring life to your website. RSS feeds are the #1 source for fresh content. All you have to do is add a little piece of code, and viola! regularly updated content! Other options include adding a news section to your front page or having users write for you.