Does it happen? I mean, we all know about bird flu and mad cow disease. Anyway, I don't happen or at least not so much as to attract real attention.
Yes, there are a handful of different diseases that can be passed down from a fish into a human (most require an extremely weak immune system) or others require for you to have an open wound inside of the water near an infected fish.
It’s perhaps somewhat more common to hear about various diseases being transmitted from birds or reptiles. They’re actually common enough to make it into medical books.
There actually is something called mad FISH disease believe or not.
It's a type of strep or streptococcus (yes, I had to google that one!)
From what I've seen and learned though, just don't handle your fish or tank if you have any breaks in your skin and you should probably be ok.
Granted, if your fish are sick and showing signs of disease.. you should probably take care of that.