My two favorite New Yorker cartoons–the second is of note because it was actually captioned by readers in a contest.
I’ve touted this Charles Addams cartoon before.
Goes with this one nicely. 
Unless you’re not from America, you will recognize “Kill-ku-lon” as a stereotypical robotic-sounding name. The same way people say Spot or Fido and people will instantly recognize that as a dog’s name. Killkulon needs no explanation. Its a robotic name and there’s a robot in the panel, it makes perfect sense.
Why would you think the robot is the artist?
I would wager that most people got that the robot was Killkulon, and most people got that Mary referred to the girl in the panel. Cultural thing I guess, I dunno. Maybe you need to watch more TV
The absurdity is played for laughs. Ignoring the caption for a moment, the fact that robots and humans date is the first inconsistency, the second being that they want to get married, and only the third being that they are related. The same type of humor is in any cartoon in which animals talk to humans. Its ridiculous, but the fact that most humans in the show treat it as nothing IS the joke. I really think you’re overthinking this
Anyways, if you don’t like that one, try these:
Found it here, for however long it’s up.
Just about any Far Side Cartoon, but “Cat Fud” is one of my favorites.
That’s evil. And hilarious.
My favorite SMBC was always this one.
Oh yes it’s ladies night…
And specifically, that “Bring some shit for my fly” panel did first appear in the Lampoon, as Elmer J. Fudd mentioned, before it was collected into a book.
Ha!
Reminds me of one of my favorite Charles Addams cartoons. It shows a waiting room with several people in it. They all are wearing shirts with different words on them. One says Godot, another says the Robert E Lee, another says 'Til The Sun Shines Nellie. Makes me laugh every time.
There is this one. Classic example of a good one-panel, no dialog, no caption, just an absurd situation.
Not sure I care for the color scheme they use, though
Ah, thanks for that, I hadn’t thought about Giles for years. In the 1960s/70s our family used to buy the annual Giles cartoon book and laugh heartily. It is a very British humour. My favourite character was the old granny - a fearsome battleaxe.
The funniest single panel cartoon has got to be the one on the right of this Tundra commic: Tundra 10-31-2010
Another Far Side
floating head
This is a good one:
I haven’t seen any Peter Arno yet. Of course I couldn’t find it to link, but I always liked the one where the seedy looking character is offering pornographic easter eggs for sale. We had a book from the 50’s or 60’s of his work. It had some pretty damn funny stuff. I’m gonna have to track that book down now…
Anybody remember those eggs that were hollow and had a hole in one end? You would look into them and there was some kind of pastoral scene or something.
No love for “The Argyle Sweater”?
Not sure the author, and it’s not argyle;
A chicken and an egg are in bed together. The chicken has a cigarette and says
I did.
I recall one where Ernest is just sitting there on the couch watching TV, and Frank walks in, and Ernest says, “Hey, Frank, sit down! There’s an old Twilight Zone rerun on!” The TV’s power-cable is conspicuously unplugged.
Reminds me of another Rodriguez toon involving a phone-bank, under the sign, “Crab Lice Hotline.” One of the workers is saying, “Now, sir, calm down. Are you in any of the following high-risk groups – filthy slobs, crummy bums, or scummy creeps?”
My fave Far Side toon is an early one: We see a street corner. On one side, a nerd rollerblading down the sidewalk towards the intersection, grooving to music from a Walkman. On the other, Tarzan astride a charging elephant leading a herd of same. Caption: “Brian has a rendezvous with destiny.”