In late June, Google's Data Liberation Front announced the launch of Google Takeout, which it called its "first revolutionary product." Its function is to let you take your data out of more than one Google product at a time.
Today, the Data Liberation Front announced that you can now take out the sites that you've +1'ed. "We’ve still got plenty more data to liberate -- including +1’s on stream posts and comments -- but we just wanted to give you a quick update," says Brian Fitzpatrick on the Data Liberation Front blog.
This could be useful if you use Google+ as a kind of bookmarking tool, but stop using the service at some point. It might be useful to have that information if somewhere down the line you're doing some research and are looking for a specific article, but otherwise can't remember it.
Google has said that +1's influence search rankings. It's unclear what influence it would have if you removed your existing +1's.
Frankly, I can't imagine that a very large amount of people would even bother, but it is worth noting. I'm not even sure how much these buttons are getting clicked on a large scale any way. I do think they'll get clicked more as Google+ gets more users, but even then, there might be some confusion as to just what the +1 button is for. I talked about this more here.
As far as data liberation goes, Google Takeout also lets you take out data from Buzz, Contacts and Circles, Picasa Web Albums, Profile, and Stream. They'll add more in time. If you want your Buzz stuff, you might want to consider getting an archive of that soon.