The bartender says, “We don’t get many of your kind in here.”
And the cyclops says, “At these prices you won’t get many more, either.”
Still loving these. Best thing I ever posted here, at least, to me.
Here’s mud in your eye, pal. How ‘bout you Mr. Ed, you want your martini shaken, or spurred? Remind me not to bet on you at the track, you’re not human enough to be a quarter-horse.
The bartender says to the Centaur “Hey, buddy. Why the long dick?”
The Cyclops says “Gimme a Bud, and a mop and bucket for my friend here.”
The Cyclops says to the bartender “I’ll bet you a Bud I can make my friend laugh.”
The bartender says “You’re on!”
So the Cyclops leans over and whispers something into the Centaur’s ear.
The Centaur laughs heartily.
The Cyclops drinks his beer and says “I’ll bet you another Bud I can make my friend cry.”
The bartender again says “You’re on!”
So the Cyclops takes the Centaur outside.
When they walk back in, the Centaur is sobbing and in tears.
The Cyclops downs his second beer, and the bartender asks “How did you do that, anyway?”
“Well,” says the Cyclops, “the first time, I told him my dick was bigger than his. The second time, I showed him.”
I guess the Centaur didn’t realize the Cyclops was a walking one-eyed monster.
A centaur and a cyclops walk into a bar. It’s a tight fit, and the centaur accidentally steps on the cyclops’s foot.
“Ow! That hurts!”, says the cyclops. “Who did that?”
“Nobody!” the centaur says hurriedly.
“Nobody!?” roars the cyclops, “I HATE that guy!”
A centaur and a cyclops walk into a bar. The bartender says:
“Don’t look now, but there’s a smokin’ hot medusa at the end of the bar checking you guys out.”
The centaur and cyclops sneak a peak over their shoulders and are immediately turned into stone.
“Told ya not to look,” shrugs the bartender.
The Centaur says to the Cyclops, “Get us a couple of beers. I gotta find the Little Foals Room.”
“Make sure your friend doesn’t step on anyone with those hooves”.
The cyclops replies: “I’ll keep an eye on him”.
The Cyclops asks the bartender “You got a Karaoke night?”
The bartender says “Not since that thing with the Sirens.”
I don’t do this often, but among a lot of excellent contributions, this one is outstanding. Very well played, sir.
The bartender leans over and says to a hot babe sitting at the bar “Don’t look now, but that tall guy is giving you the eye!”
Agreed.
I don’t get it. 
“Martin” - it’s like a martini but with only one i…
A martin is a martini with one i.
Aha! Witty. Very, very witty! 
The Cyclops says “Gimme a Bud Lite.”
The bartender says “We quit selling that when they put an Amazon on the can.”