I am seeing some reports from Webmasters that the link report in Google Webmaster Tools is reporting a much smaller fraction of links.
A Google Webmaster Help has one webmaster complaining a drop from 7,000 to 4,000 reported links.
I checked this site's and we dropped from almost 4 million links (I am not sure how many I had recently here but June of last year we had 3.8M) and now it is just above 2 million. Not that it bothers me. But it does show that the link counts have dropped and I am able to confirm it on this site.
Google Webmaster Tools has had this issue several times, including June 2013, February 2013 and other times.
So if you see your link count drop significantly, do not worry. It has no direct impact on your rankings. "It" being the reporting in Webmaster Tools.
Forum discussion at Google Webmaster Help.
