My Mac, too, was rendered essentially unusable by MacKeeper popups when I had installed nothing. I don't recall how I eluded them because it was many months ago, but I am writing to tell you that I managed to ward them off permanently by installing ghostery (http://www.ghostery.com/), a free browser plug-in that keeps MacKeeper popups and many other browser nasties at bay.
I have no affiliation with ghostery, and no idea what their business model is that provides such an incredible product for free, but it has kept my whole family's and business's web experience much cleaner since deploying it on all our Macs.
Ghostery's deafult settings have it pop up a brief (purple) alert window on every page you visit that tells you everything that the site is trying to do out of sight within your browser. I eventually found this annoying and easily located the setting to change so it doesn't display anymore.
Hope that helps everyone and isn't some form of malware in its own right.