No crawler I know of accepts a redirected robots.txt from an alternate domain for rules about the original domain.
You also might be able to fool Google Webmaster Tools or other utilities into thinking you own bit.ly. One of the authentication methods I've seen used was the creation of an empty html document in the root directory.
The 1997 internet-draft (never an RFC) suggests the redirect should be followed, but the potential confusion that could cause has meant few, if any, crawlers have followed that guidance. It's more likely to be a webmaster configuration error than real intent.
And what about sitemap.xml, atom.xml, and other typical files that could also be redirected?
Why not try it? As of this writing, both of those go to other places.
I checked the other one that lept to mind, favicon.ico. Bit.ly appears to have hardcoded it (probably in apache configuration or equivalent for whatever server they use), however, try http://bit.ly/faviconico and look at the resulting URL. Looks like a few things were tried by the same guy. Now, pwning the favicon would have been cool.
I've started to see them used in email sent internally by Corporate folks at my company, as links to press releases on our own website.
For us hackers: When sending plain text messages, you should encase urls in <angle_brackets> to prevent breaking and especially the trailing period problem like <www.google.com>.
Hundreds of thousands of "direct" hits, and hardly any actual referrers. Looks like bit.ly is counting crawlers as hits. Not too surprising given the lack of validation elsewhere.