The hit counters are intended to measure popularity of the chess site by number of hits the page received from the counter home page and vice versa. However, they are vulnerable to cheaters promoting themselves all time long by self-clicks. Nowadays there aren't many interesting hit counters around the Web. FIDE used to have their own one, but unfortunately it disappeared. Those listed below are all that I found. Most of them are just local hit counters, some of them are probably not active any more.
The webrings are sort of automated link list. Web sites dealing with related topics compose a ring and everyone links to other partner sites. Unfortunately those do not seem to be popular either. There aren't many chess focused webrings and rather few chess sites are in there.