I came across a website of a company that does personalized widgets. Visible front end content is all about getting your own unique widget etc etc but nowhere does it contain anchor text or any mentioning of the online widget store it has hidden in the source code...
The source looks like this (URL hidden for obvious reasons):
There are good, bad and even some ignorant reasons for hidden backlinks.
A good reason to use hidden backlinks is to help crawlability. Imagine you have a 100% flash website. Search engines would have a hard time crawling it, so some webmasters hide backlinks to help them crawl it. Personally I would just avoid using flash.
A bad reason to use hidden backlinks is because some webmasters read a 12 year old blog article that spoke about the easy way to trick the search engines using hidden backlinks. The search engines have become alot better in spam detection (but still not perfect). So some webmasters are blindly following out dated seo advice. This is also why you see some webmasters still spending alot of time spamming meta keyword tags. Just because someone else is doing it does not mean its a smart idea.
What would an ignorant reason be? Remember I said the search engines spam detection is not perfect. Smart spammers know there are still a few tricks they can use. Some of these spammers will hack into a website (usually wordpress or another cms) and hide hidden links to their spam sites in an attempt to steal link juice. Unfortunately, these ignorant webmasters do not even know they have been hacked.
These are just a few of the many different reasons you'll come across hidden links. You should decide what is your business strategy and then think about the short & long term risk/reward for hidden backlinks.