I think most of the time when a move is unexpected - apart from those times when the player is unfamiliar with an idea, or the move is just a blunder - it is because it would ordinarily be a bad move, but something about that particular case makes it not so.
We might normally expect a move to be bad for instance because it loses material, because it jeopardises king safety, or because it doesn't appear on the surface to serve any real purpose. I am going to show some examples of moves that would not only seem bad ordinarily, but actually downright absurd.
Warning: These are quite difficult.
White to play and win - Wotawa 1955
White mates in 4 moves - Ernst 1935
1.Ng2! hxg2 2.Rg3! hxg3 3.Bg1! gxh2 Bxh2#
This last example comes from a game I had recently. I was black against Chris Wallis in the Ballarat Begonia Open. The solution should be relatively easy to find given it was played in a game, but apt nonetheless.
White to play and win - C. Wallis vs. A. Brown 2014
For a beautiful rendition of heroism in chess, Sam Loyd style, see this post.