Tim sends Eric an email stating "omg check out this new site u have 2 see it!!1!"
Eric, not being the sharpest knife in the drawer, clicks the link and spends the next day trying to unsee what he's just seen. Another use is FBI redirection.
Tinyurl lets you choose a custom redirect name such as
tinyurl.com/hotgirls, make use of this when posting on certain forums. For example if you're posting a link to a new Grand Theft Auto/World of Warcraft trailer, make the link something like
tinyurl.com/wowtrailer. Sadly most of the good ones are already taken.