Howdy!
In the midst of communicating with Google because of a robots.txt issue, we had a bit of a backfire of sorts and received a notice of unnatural links. It's not a horror story or anything. It's seems more like, "Hey, before we address your other issues, here is something you should clean up" although I don't dare put words in Google's mouth.
A few years ago we hired an SEO company which shall remain nameless who did some anchor text blog posts for us which at the time, we had no idea was an issue.
There aren't an enormous number of these links hanging around, but checking our anchor text, in OSE, we saw that there are around 50 or so. We decided to use removeem.com as an easy way to request removal of these links.
However, on first run, removeem returned a large number of anchor text links beyond just these obvious ones that are actually natural links from users, fans or those that sell their goods on our website. Examples of these anchor text links would be:
"DEMO"
or
"Find My Products Here"
or
"Home Page"
http://www.mysite.com/goodstuff/foryoutubuy/html
We are a media selling site and we do have a lot of download sites that attempt to "share" content and link back to us via a DEMO link, etc. While these aren't the greatest sites in the world, they are nevertheless natural links. Heck, they are pirating our goods, shouldn't we at least garner the link juice from them?!!? 
So, questions: Should we remove all of these links as removem.com suggests or only remove the ones that are unnatural and clarify with google that these other links are natural?
Thanks for your help!
Craig