Why are some checkmates more beautiful than others? Is it simply the rarity with which they can be executed in real games, or is there something aesthetically pleasing beyond that?

Only beginners get checkmated good players resign when they know they have lost it and can't do anything about it, checkmates some times appear a part of beautiful combination about which the opponet must be thinking long time back, when we cannot even guess of what's going in his/her mind.

I prefer to let my opponent perform the checkmate if it seems to be forceable in the next five moves or fewer. It is the most satisfactory resolution to a chess game (at least, for the winning player), and it seems petty to deny it to an opponent who has all but played out last few moves.

I prefer it when my opponents resign when I have a winning position. Playing out the last few moves seems like a waste of time. It's as if my opponent is saying you've won, but I won't go down without annoying you!

I don't see it that way at all, but that's probably because of miscommunication. If I have blundered material but it will take a dozen moves to press the advantage into a win, I will resign. But if there is a mate on the board that I can see, I let my opponent have it. That ties in with the subject title. Checkmates can be pretty, whether it's as simple as a back rank mate or the combination in the 19th century "Immortal Game".

The general consensus I get from World-Class (or perhaps 1-2 levels below World-Class) Calibre tournaments is that the polite thing is to resign in such situations, except perhaps in the case of an absolutely stunning, brilliant mate, which it is sometimes considered gentalmanly to allow the opponent to execute. However, such things don't really creep up too much anymore...

 I only see it that way if they just start tossing away all their pieces.  That does seem rather annoying

WanderingWinder, I'm not anywhere close. My opponents do enjoy a checkmate and don't mind playing a couple moves of chess, which they play for fun and not for titles.

For the record, I've resigned at least 10 times more games than have been resigned in my favor on the chess.com site. I don't mind doing so.

I wasn't trying to imply that you were. But chess culture generally flows from the top down. Also, I would ask how you know that your "opponents enjoy a checkmate and don't mind playing a couple" extra moves? Personally, I can think of maybe one time where I actually preferred giving mate to accepting a resignation, and definitely none in CC.

I don't know. I guess I imported assumptions from my Over the Board play.

I know I typically set up Conditional Moves on chess.com if I see a forced mate in 2-4 moves, so it doesn't make a difference to me what my opponents do in those cases.

I just reread this thread.

Bugger me for taking the bait. It was quickly derailed from the question of "pretty mates". That would have been interesting to read, if anyone commented on it.

Pretty mates and combinations:

 http://www.chess.com/video/player/beauty-and-entertainment-1

What is beauty?

What is kiss?

Spectacular mates come from good, effective combination moves.  You will know it...

Keep it super simple?  Or Keep it simple stupid? 

What is love?

Not only does it give personal satisfaction, but it degrades and humiliates your opponents, especially if you are sacrificing pieces. Humiliating your opponent is the next most importnant thing to winning

Wow (I didn't know love could be like that).

Baby, don't hurt me.
Don't hurt me.
No more