I know that there are plenty of sites out there that offer free counters and we really appreciate our customers

! While we do require a text link with every counter, we really do not enforce it 100% - around 99.99%, just kidding

. We are supported by our advertisers so we really do appreciate those who do put the text link on their site.
What I don't get is when a counter service offers counters with hidden links on someones site. Either using hidden text or by placing the text within <noscript></noscript>. Generally most search engines do not like hidden text or links so those counter services are putting their customers at risk. I just don't get it. Just be open about it and most will use a counter service per their terms.
If I were you, I would watch out for those hidden link especially if they are linking to some unfriendly territory.