'I have come to the personal conclusion that whilst all artists are not chess players, all chess players are artists' - Marcel Duchamp.
Favorite chess quotes

"When I am white, I win because I am white. When I am black, I win because I am Bogoljubov." -Efim Bogoljubov.

There's also Tartakower, who gave us lots of interesting quotes:
"All chess players should have a hobby."
"I never defeated a healthy opponent"
"I talk to myself because I like dealing with a better class of people." (Not very chess related though)
I do not think that the Morphy quote is authentic. There is a somewhat similar comment about billiards that has sometimes been attributed to Herbert Spencer.
"Moderate skill in billiards implies a certain amount of mental capacity, but such skill as you have displayed is clear evidence of a misspent youth."
I think the authenticity of that quote has also been questioned.

(my chess teacher looks at kid's board) "Oh wow, your kingside has so many holes it looks like swiss cheese!"
One of my favorite chess-teacher chess-related quotes.

”Misha was so ill-equipped for living... When he travelled to a tournament, he couldn't even pack his own suitcase... He didn't even know how to turn on the gas for cooking. If I had a headache, and there happened to be no one home but him, he would fall into a panic: "How do I make a hot-water bottle?" And when I got behind the wheel of a car, he would look at me as though I were a visitor from another planet. Of course, if he had made some effort, he could have learned all of this. But it was all boring to him. He just didn't need to. A lot of people have said that if Tal had looked after his health, if he hadn't led such a dissolute life... and so forth. But with people like Tal, the idea of "if only" is just absurd. He wouldn't have been Tal then.”

I really don't like the chess players in general. They're not my kind of people. They are very petty. They're mean-minded, petty, small-minded, stupid...
Robert James Fischer

Never resign! ~ Chess beginners and patzers
To be fair you also get GMs on this site dispensing that advice, and although "never" is a pretty strong choice of words it does have some merit for us mere mortals. I know I've personally won quite a few lost games because my opponent blundered or timed out or whatever.
On that note, how do you define a patzer? I know the general definition is a bad player, but that's pretty relative.
"The ability to play chess is the sign of a gentleman. The ability to play chess well is a sign of a wasted life." - Paul Morphy
That's my favorite quote, whats yours?