URL root question

Will SE's pick up pages that have shorter roots and list them better and more quickly?

i.e.

http://www.mysite.com/

vs.

http://www.mysite.com/folder/

vs.

http://www.mysite.com/folder/folder

It may have some affect on smaller engines, but no, I really doubt any of those would make a difference. There are more important things search engines use such as how sites link to you, the number and quality of sites linking to you, the and amount of content on your site.

A few people think so, my personal opinion is that it is not the depth of
the directory structure, but rather the depth of the linking structure.

Usually, pages that are deep are not linked directly from the homepage,
and I think that is what makes the difference.

Bompa

I think depth has more of an indirect influence rather than being calculated as a particular factor by Google. I think Google is quite happy to crawl a site that is many pages deep, as long as the site has a high page rank and is linked to from many sources. For instance, a direct link from an external source into the depths of a website will get crawled more frequently than a page without any external inbound links that takes a few clicks to get to from the homepage.

pompei is right on the money

Although...I don't really see many sites popping up high in the search rankings that have long url's in site/directory/after/directory

That could be the correlation between link and directory depth.