Depends on a number of factors..
How many links have you pointing to your site?
How old is your site?

If you have links pointing to your site and you have a new site I would suggest about 3 months for you to get page rank on your site.

Page rank for a new site is not important. The trick is to see how quick you can get the site to rank in the search engines..

Sam

PR updates only happen once a quarter. To be honest I'd be surprised if all your site pages are even cached after only 20 days. Be patient.

To be listed at all should be pretty instant. (one of my new sites was in a matter of hours)

Get some backlinks so Google can get to it.

If youve got some links from high PR sites and hubs then the site will be indexed quickly. You should submit an xml sitemap and sign up to Google Webmaster Tools as well. Sites can appear and rank for low competition keywords in a matter of hours as michael says. With regards to the PR, your PR is being updated on a regular basis but this value is only exported to the tool bar every 3/4 months.