The 110 most fantastic moves ever played

...is an online collection by the fabulous Tim Krabbé.  (The link goes to fantastic moves 101-110; you'll find links to the rest of the list at the bottom of Krabbé's page.)

He really should have included Frederick Rhine's favorite move.  But all "best" lists are necessarily imperfect.  (Edited in a few hours later: in the comments, Frederick reminds me that Burn's move was only recently rediscovered by his chess biographer, Richard Forster, and that Krabbé himself said that it belonged near the top of his list. Krabbé discusses interference sacrifices similar to Burns's—check out the amazing move that Peoria native, and newly minted Life Master, Pete Karagianis dropped on a Grandmaster!  It's not a Novotny, and it doesn't win by force, but it's mighty purty.)

Karagianis-Anka, 2004 National Open

White to play and astound (though not necessarily win)

John Emms liberally "borrowed" from Krabbé's site for his 2000 book The Most Amazing Chess Moves of All Time.  On Krabbé's home page Chess Curiosities (where you'll find many days of fun reading) he refers to his 110 most fantastic moves collection as "his most frequently emmsed page." If you prefer books that aren't plagiarized, I can heartily recommend  Secrets of Spectacular Chess by Levitt and Friedgood.  (The first edition can be bought used for a pittance.)

The most astounding move of all time

Cover up the moves in the game below and look at the diagrammed position. Amos Burn, one of the world's best players toward the end of the 19th century, playing Black, looks to be dead lost. White will regain his sacrificed piece and mate Black in short order, right? In this seemingly hopeless position, Burn found what I consider the most astounding move in chess history. (To clarify, I mean astounding good moves. No doubt there are lots of astounding bad moves - say, where White could have mated in one and instead played a move that allowed Black to mate White in one.) Do you see it?

Chess problemists will tell you that Burn's move 33 is an extremely rare example of the Novotny theme in actual play. That is, 33...Qg4!!! moves the queen to the square that is the intersection of the d1-h5 diagonal controlled by White's bishop, and the g-file, controlled by White's rook. If the rook captures the queen, it blocks the bishop, allowing 34...Nf3+ and 35...Nxd2. If the bishop captures the queen, it blocks the rook, allowing 34...Bxd2. There are two other plausible continuations: 33.hxg4? allows Black to win the queen either way, leaving him with an extra piece, and 33.Qxg5+? Qxg5 34.Rxg5+ Kh6 wins a piece for Black. Note that (as Burn pointed out) 33.Be4! would have deprived him of this resource, winning easily for White.