GitHub publish a copy of all the DMCA takedown notices GitHub receives.
One thing I found very interesting was looking at their graphs showing the number of commits over time.
Of course, this doesn't necessarily mean that DMCA takedowns are being issued more often in general, it could simply be a reflection of GitHub's own growth over time. Personally, I suspect it's a mix of the two, both that GitHub is becoming a more popular place to store things online, and that more and more DMCA takedown notices are being issued every day.
I think that our copyright system is badly broken, in particular the approach that many sites (not specifically GitHub1) are forced to take is very "guilty until proven innocent" where content is removed first with the option to appeal later, and there is little recourse against organisations that submit inaccurate takedown requests.
However, I find it hard to get too worked up about the notices on GitHub, having looked through a few of them, most seem to be fairly tightly targeted and aimed at a single repository of clearly infringing content. In fact I was surprised how many of them were for .pdf copies of books and not for code at all.
GitHub actually have the phrase "Users identified in the notices are presumed innocent until proven guilty", although I'm not sure exactly how that works. If they are getting less than 40 per day it's conceivable they have a real human being looking at each of the notices. Actioning the ones that are simple and investigating or flagging ones that might be a grey area. ↩