I've seen the topic of appropriate use of TinyURLs raised several times this week and I have been giving it some thought. The real catalyst for this post was a blurb on Slashdot that I read this morning about TinyURLs (and the like) weakening net architecture.
TinyURLs are a very handy tool and completely appropriate for may applications - shortening URLs for email or text message transmission, etc. However, some uses are questionable. It would probably not be a good idea to use TinyURLs for articles (especially in print publications) or as links between web pages.
The reason is pretty simple: there is no guarantee that these "aliased" URLs will be survive for any significant period of time. In fact, it's almost given that these links are ephemeral. If everybody used TinyURLs on their web pages to link to other web pages, the web's functionality as designed would fail if the service running the TinyURLs failed - i.e. there would be a single point of failure.
Also, consider if some company purchased the system (e.g. TinyURL) that operated all of these aliased links. It could result in numerous infringements on the freeness of the web.
Anyway, here's the point: TinyURLs are great for using in emails and text messages; you should really think twice about deploying them on web pages or publications. Just my .02...