What happens when you earn all the badges?
By any chance, is there some sort of 'hidden' badge for earning all the badges?
It's going to be nearly impossible for anyone, save perhaps the founding members, to get all the badges, since you have to be a founding member to get a few. Also, you'd have to get all the tag badges, at which point you'd have millions or billions of rep..
Also, it's impossible to get a badge for having all the badges, since you don't have the badge that signifies that you have all the badges.
I sense a recursion joke in there somewhere.
I have to double check this, but I think earning badges like Unsung Hero and Tenacious would be mutually exclusive to this, since they would indicate a lack of voting on a significant number of your posts (a requisite for quite a few of the other badges). I'm not certain it's impossible, but you'd need to do it in a very planned and calculated way. I'm not so sure earning all of them is possible.
No, there aren't any hidden badges (period). We've been discussing the idea of additional gold and silver badges that wouldn't be on the badge list, but discovered by earning them or happening upon someone that had. By design, these would be extremely difficult to get. It looks neat on paper, but some feel strongly against the idea, so it's still just an idea at this point.
I've also got ideas for badges that sites themselves could earn, like 'Happy Place' for great new user retention or 'Speedy Gonzales' for consistently low median times to the first up-voted answer to new questions. These would hang on a different wall showcased more as community than individual achievements, while those that participated heavily in earning them could possibly get individual gold / silver badges for doing so.
All still an idea.