Summary: It's often very desirable to see what links people are clicking on. Redirection services can often provide that information.
Can I track what links people are clicking on, even if they go off my site?
You bet!
There are a class of services on the web that were originally intended to provide a way to replace an excessively long URL (Amazon.com book references are infamous for this) with a much shorter one. They do this by providing a redirection service ... you give the service a URL, and you get a token back. Then instead of linking to, or telling people about, the huge unreadable URL you started with, you give them a link to the service that includes the token. The user ends up at the same place as the big long ugly URL, without having to have even seen it, much less type it in.
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Why am I talking about redirection when the question was about link tracking? Because some of these services will give you exactly what you're asking for - detailed reporting of the traffic going through those links of yours.
Newsletter publishers, by the way, get another benefit. Should the target of your link change, you've previously not had a way to correct all the now-broken links you've emailed out. Not so any more - simply go to the redirection service, and update the old token to it's new link, and everything is working once again.
If you're curious how this works, or if like me, you're a do-it-yourself kinda person, you can have a look at a simple CGI script that handles redirection - redir.pl. You'll have to add your own reporting and such, but it could be educational, and perhaps even useful in many instances.
Article C1830 - August 15, 2003