Question: Recently there has been a lot of hype about URL Shortening. I guess some URL Shortening services even offer tracking stats. But, doesn't adding one more level of look-up to the original URL affect page ranking in any way? Just curious to know.

Answer: 
IT depends upon the implementation from the URL shortener service. If they use HTTP 301 and/ or HTTP 302 in their redirects then Google are quite good in interpreting these correctly in accordance to Page Rank. However other parameters might be affected by URL shortening.

Most Search Engines uses anchor text and URL texts as a parameter to what to give hits for for a specific URL. And if the URL changes from <http://example.com/some-article-about-C> to <http://example.com/234432> then obviously the first one carries more information for the search engine which will make it perform better for "article" and "c"...
It might, right now, but I wouldn't expect that to last for too long. SEO and PageRank are subjects where a lot of guesswork is passed off as wisdom.

If you're that obsessively worried about your PageRank, here's what you do. Take that energy, and put it into creating content that people want to link to. You'll get better results.

People buy stuff. Robots don't.