There is a slight correlation, but there is a correlation between the PR of your backlinks and your SERPs.

Short answer is yes.

Long answer is it depends on a whole lot of factors.
The keyword for one - A Low/orNO PR site that is a optimized for a keyword can usually beat a high PR page that is not optimized for the keyword, but ranks for it anyway.

So you should only worry about PR when:
-doing keyword and niche research of your potential competing pages.
-if you plan on selling your site in the future, or you want to sell Backlinks.

I would say no, not really.

PR is passed on to your site from backlinks on high PR pages. Essentially the PR flows through to your site and builds trust with Google.

This PR trust used to be a big contributor in your websites rankings, now, it doesn't carry as much weight.

So, yes, it does have some link to your rankings but not directly.

Dave

Yes PR does have some correlation with SERPs *if* you have your onsite optimization dialed in.

Its important to understand that PR is an indication of Google trust, the more the PR generally the better your opportunity to rank.

Whilst there might be some tenuous link I believe far too many people go after a high PR ranking. It is much better to concentrate your effort with providing good clear natural keyword rich content and many backlinks correctly tagged with your keywords.

I believe that pages with a high PR tend to get diluted when links from them are sent to sites with lower PR which is why people try to link to high PR sites to share in their success. I have not bothered about PR for the past 5 years but all my sites have been gaining success in keyword searches.

I think also the fact that you can be number 1 without any PR, or way down the list with a high PR cements the fact that PR is not something to put all your concetration towards if you are aiming for top rankings.

Google PageRank is probably one of the most important algorithms ever developed for the Web. PR is based on quality links of the site and Google SE has the only one that has it and other SEs don't have. PageRank is only one of numerous methods Google uses to determine a page’s relevance or importance.

I'll offer a contrary view... I have found PR to be very helpful when searching for link partners. High quality links from high PR sites are still valuable.