Do any of the Blog publishing platforms expose API's where we can get a continuous feed (or search through the feed) of blogs being written? As far as i read through the API of blogger.com i don't think they expose API of this sort; you can probably get a feed of blogs written just by your friends but not by all public users.
Also are there any 3rd party APIs that crawl the blogosphere and provide feeds of this nature for free?
The various sites Ping-o-Matic targets do this. Some have APIs. None will be anywhere near comprehensive, but there are enough blogs out there that comprehensive would be impossible to process for anyone not Google/Yahoo/Facebook/etc. anyways.
(PubSubHubbub is) a simple, open, server-to-server web-hook-based pubsub (publish/subscribe) protocol as an extension to Atom and RSS.
Parties (servers) speaking the PubSubHubbub protocol can get near-instant notifications (via webhook callbacks) when a topic (feed URL) they're interested in is updated.
The video and the 10 slides in the above link may prove more useful than my explanations :)
The protocol was created by Googlers, because, even with 2 million servers, it's hard to follow millions of blog feeds and now approx 150 millions of gmail feeds (Google buzz ...) and so on, not speaking of the server load due to bots constantly inquiring about news for real-time indexing and search.
Three months ago, it was already used by the following publishers: Google Alerts, Reader and Buzz, Blogger, FeedBurner, Wordpress and Typepad and from the wiki page Companies using it: LiveJournal and Myspace.
The wiki page Comparing protocols talks about differences and advantages over existing protocols XML-RPC ping, changes.xml, SUP, SLAP, XMPP pubsub and rssCloud.