For iPhone ios users you can go into each app individually and change the notificiation settings. That's a bit time consuming if you have a lot of apps that use Badges.
For android users it looked like going into the Badges app and Force Stopping would work, but that was short lived as the next notification on Facebook I received just reset it (without the ability to disable Badges at all...hmmmmm). So for now I have moved my social media apps to the last screen on my phone because it is the one I flip past and to the least. This should deter me from app checking and clearing those pesky red circles at least for a while. Maybe the next step is deleting *gasp* and removing these time draining apps all together.