There are a range of issues with that but the few that spring to mind immediately are:

1) Pasting into an IRC channel as already noted by someone else and;

2) Pasting text where formatting is important (such as a code snippet) into an email

The latter is of particular importance when sending through things like "tags" (ie. javascript snippets) to be embedded in HTML pages for things like analytics, conversion tracking, Wufoo forms, Wistia embeds and the like. If the formatting is off on a lot of that stuff because people have been copying and pasting it in and out of emails then they can end up not working at all.

NOW ... the advantage for me over something like pastie.org or pastebin is that when I paste a snippet into a Basecamp todo list item, for example, I'm creating an external dependency on those services for some or all of the relevant data to the todo list item.

By having a service which embeds the data into a URL that can then be decoded into it's original format without error, using something that I can reimplement myself if the original service should disappear, I end up with a much more "future proof" and reliable storage of that format sensitive information.

IRC chat would be my guess. Since data isn't stored on a server/can't be taken down, this seems like this could be useful in the shadier IRC rooms sharing questionable content.