Although opinion is much divided, do you see any benefit to using subdomains for blogs (blog.domain.com over domain.com/blog) as opposed to subfolders, or vice-versa?

Question answered by Melanie of Cog SEO Blog (with additional comment from Tim)
Reasons for using a sub domain

• Use a sub domain if the blog’s content is not closely related to your main site as not to dilute your theme strength
• Sub domain pages develop their own PR spend. The parent domain will only bleed PR to the sub via a link, and the transfer ability is most likely less. The transfer can be stopped by only linking to the sub domain via nofollowed links.
• Sub domains can be on a dedicated IP, or separate c class increasing the backlink value from site to site ( I would recommend linking in to the parent domain from the blog, and nofollowing out from the parent domain to the blog) One way links are preferable.
• Users can be confused by sub domain addresses. If you use a sub domain I recommend you link to it as is it was part of your main domain design and back from the blog in the same manner to decrease confusion. You do not want the blog to be an island.
• Link relevancy between the sub domain and the parent domain is more difficult to establish. Care must be taken to maintain the relevancy, unless you want your blog to be an island.

Reasons for using a directory

• Directories are easier to manage
• Directories add to your site’s total content and how your site is “viewed” by search engines as a whole
• Pages within a directory will accumulate PR from the main domain pages through your links to the pages…Like menu links for example. You can control this by using a nofollow on the links to the blog’s pages. I believe PR flows easier from your own domains pages into your own domain’s pages.
• Backlinks accumulated will be added to the parent domain’s total
• Directories are easier to promote/market and generally users with remember and use the domain address and click through from the main page, thus enabling your ability to deliver additional content and ads more easily…Making the promotion of the entire site easier.
• Links to your directory pages and back are innately more relevant

So to answer the question, a directory is the best choice for most situations. The only time a sub domain would be more beneficial is if the content of the blog tends to be unrelated to the theme of the parent domain.

Some questions will be raised in the coming months about this issue as; Google moves to limit the amount of a domain’s pages within the search results to 2 pages per query. This is said to include sub domains at some point. Matt Cutts announced a PubCon that “only 2 urls from the domain” will be displayed. The interesting question will be…Will sub domains on a dedicated IP, or separate c class, be missed or excluded, or will it be a url based algorithm. We might even see more sitelinks than we have in the past. This is defiantly a wait and see deal.

Additional notes from Tim
With the recent announcements that sub domains will be treated like directories everything has been thrown in the air. However if they are truly being counted as directories that would indicate inbound links to sub-domains will count towards the site overall, which could mean sites with lots of sub-domains seeing a sharp increase in rankings for their main site and a more even ranking across the subdomains. Expect wordpress.com and similar sites to get a temporary boost both to their main site and to the sub domains which hold peoples blogs. In other words expect to see a lot more spam in the index over the next few months.
UPDATE: Matt Cutts has added some clarification on his blog.