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When it comes to Google, PR is relevant to improving your positions. But, its not the only thing! It's an important part of the process and one that is closer to the top of the list of things to do.
Inbound and outbound links are what makes the web. Of course the more inbound links you have, the more traffic that is generated for your site. When Google released the Toolbar and made us aware of PageRank, the value of those inbound links became the topic of discussions.
PageRank is still an important part of the overall equation. It is not everything, but, that one extra PR point can make the difference between a #1 and #2 spot when the competition gets fierce.
If someone tells you that PR is not relevant in regards to your position in Google, just do a search for some of the more competitive terms and you'll find your answer.
When it comes to less competitive terms, PageRank sort of moves down the list of priorities and other factors come into play. The statement I've seen posted here many times is that there are over 100 factors that Google takes into consideration. I've not seen a definitive list of these 100 factors and I doubt that we ever will. But, if you look at the first 20 basic rules of engagement, I think that covers the priority factors! ;)
