They never expire. Of course there is always a chance that the service will die and the domain will be acquired by somebody with entirely different goals, but then there is very little in this world that is truly permanent.
A year from now, when someone is searching the archives, will they still be able to follow a tinyurl? Three years from now?
The *original* URLs, especially the ones we are using tinyurls for, usually don't last/become uninteresting in a fraction of that period of time.
There is always the internet archive (http://www.archive.org) to help with this. But this particular thread of the discussion is a moot point anyway, since if you can go through the trouble to investigate where a lost page went, I'm sure you can go through the trouble to figure out which URL tinyurl.com is redirecting to (even if you get a 404, you should be able to see the real URL in the URL field of your browser, or telnet to the server and catch the redirect if you have to). In any case, both sides have had too many good arguments to be able to come to any decisive conclusions, I think. But at least, I hope fellow boosters have been nudged to exercise some moderation in the use of tinyurls. No reason for obfuscation if the URL is already short enough (and in my own very personal opinion, 60 characters or less should be short enough). /Mattias