The maximum amount you can win on Jeopardy! is as follows:

The total dollar value on the board in the first round is 6*($200 + $400 + $600 + $800 + $1000) = $18,000. For maximum winnings, the Daily Double clue must be hiding behind the least dollar value ($200) and be picked last, so the maximum doubling total is $18,000 - $200 = $17,800. Therefore, the maximum you can have at the end of the first round is 2*$17,800 = $35,600.

The total dollar value on the board in the second round is doubled to $36,000. For maximum winnings, the 2 Daily Double clues must be hiding behind the least dollar value ($400), and be picked last, so the maximum doubling total is $35,600 + $36,000 - 2*$400 = $70,800. Therefore, the maximum you can have at the end of the second round is 2*2*$70,800 = $283,200.

Final Jeopardy is simply a doubling stage, so the maximum you can win on Jeopardy! is 2*$283,200 = $566,400. Not too shabby! Next to impossible to achieve, but not too shabby at all.