Are there any legal positions known to be impossible to come to in a normal game? There are some fairly obvious ways to set up a chess board that cannot possibly happen:  both kings simultaneously in check would be one.

There are some positions that seem impossible in a normal game... for example, one side has all of it's original pawns in their original location and the other side has NONE of its pawns remaining - but with both sides displaying all pieces in their original positions (perhaps knights can do this, I don't know.)

However, seems like there may be some impossible positions that are not at all obviously difficult.  

The question is if there are any known legal positions (preferably ones that  a normal human might think are the result of a game) that cannot be played into?
Hi and thanks for the question. The words "legal" and "illegal" are actually defined in the FIDE rules. Basically, a legal position is one which can be reached by a sequence of legal moves.

So, with this definition, I think that you are asking: are there illegal positions which aren't obvious? The answer is "many" Welcome to retrograde analysis! :D

There is already a chess.stackexchange question on this, so I suggest we continue the discussion there: Are there any illegal positions that are difficult to spot?