Curious to know how these tiny URLs help or take away from SEO efforts? I know they make long, ugly URLs look more pretty but does using them in a backlink situation take away from potential link juice? Do they work the same way a 301 redirect works or is it different?

Some of our URLs get quite lengthy and the thought of shrinking them would be nice, although people wouldn't know what they were clicking. If the benefits of using tiny URLs are similar to regular URLs, it may be worth experimenting with.

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Well we have not even tested it so far. Just for being safe side, avoid the tiny URLs in the internal linking. But i found no harm in using it in the social networking sites.

In all the social networking sites many using short url i also using that its working fine

TinyURL tantamount to NO Link Juice...that's pretty much a fact.

If you would check Google Analytics, they show the referral from Tiny URLs in that name of the tinyurl site only and not the site you are intending to.