I notice that many websites now display logos to suggest their pages are valid W3C (x)HTML markup. How important is it that the pages of my site pass W3C validation? Will I get more top ranked results with validated markup?
Roughly half of all the pages on the internet today would fail W3C validation. Inherent to the nature of writing any kind of code, is errors. They just creep in there. Writing HTML markup is no different, but thankfully it's more forgiving than code VB, or C# code. Even most of the sites that display W3C validation logos have actually got markup errors that would show up if they were put through a validation checker.
The good news is that no search engine is going to dump half of its index, simply because the pages didn't have valid markup. What's more important to the search engines is the quality of the content. As it should also be to you; content and accessibility.
If you can write valid code as well as quality content, great. However, your primary concern should always be to write the great content. If having written your content and you want to do everything you can to improve your site, then after everything else you might want to consider checking your pages for valid markup.
Google doesn't have a trigger for valid markup, meaning you won't achieve higher rankings for having valid markup, because it really doesn't matter that much to search engines. That may change in the future, but it's unlikely.