So, you can capture any piece in chess except for the king. But what happens if me and my opponent get all pieces captured (except for the king)?
Since you can't move your king into check, you can't legally check the other king.
The Laws of Chess, section 5.2b, states that:
The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7.
When you only have Kings then you can take a tour of the entire board till the end of the World without any hesitation . :-) (Just Joking ) .
The Game at this point is a DRAW . Since neither Player can play without any objective and Game of Chess is all about Checkmating your King then without any material resistance it is DRAW . Infact a lone King with a Knight or Bishop and also against another King is also a DRAW material is not sufficient to Capture King .