Fan Works / Sarcasm Blind

Cloud Kicker in Ace Combat: The Equestrian War acts like that at times.
A Different Kind of Truth: Both Teddie and Gyro take Johnny's sarcastic quips and comments at face value. In the former's case, Johnny lampshades it by thinking that bears don't seem to understand sarcasm.
Princess Zelda sometimes shows signs of this in Paper Mario X. Example from chapter 41:
Koopatrol: Oh, would you like to be in the quiz?!
Zelda: OH... a quiz? It's a good test for my wisdom—
Koopatrol: I WAS SARCASTIC! We only need one person!

In Half Past Adventure, Dr. Minerva Campbell appears to have trouble registering sarcasm, interpreting a joking comment about someone who's taking too long in the bathroom as a request to send out a search party.

Xanatos gives us Linda^note, who, while not totally ignorant of it, at least needs to be told when someone is being facetious. Naturally, she interacts a lot with Matt.

Family Counseling With the Dursleys:
Harry: I was hiding out here so that no stupid oafs would come over and talk to me. But I guess my plan was foiled.
Dudley: Why? Who found you?
In Gypsy Caravan Barty Crouch Jr. comments on how hard he's been trying to stay out of Voldemort's way when the latter is busy, prompting Snape to offer to bring a book next time he's called and Crouch to reply that that would be lovely and sincerely thank him. Snape's final thought as he departs is that sarcasm is wasted on the insane.
In Harry Potter and the Angry Grim Reaper, Ron insists that Harry can't be the real Harry Potter since he doesn't have the scar or glasses.
Harry: What did you say your name was again? Bilious? Well, gosh, you're right, Bilious, you caught me out. My real name isn't Harry James Potter, it's actually Fool Foodchomper. Come on, Hermione, let's go.
Ron: I knew it!

For the Glory of Irk: Lard Nar seems to be totally incapable of detecting when somebody is being sarcastic.

The Emancipators: Tenya doesn't understand sarcasm very well. After learning this, Izuku offers to help him learn how to identify it by signaling him whenever he's being sarcastic.

Anthropology: Lyra does not understand sarcasm, and actually has to be informed when someone is being sarcastic with her. Example from chapter 23:
Lyra: I was reading that history book you gave me and it said that America had been in wars. A lot of them, actually.
Paul: News flash. I've never heard that before.
Lyra: So... It wasn't true? I mean, if there had really been so many, you would have heard—
Paul: That was sarcasm, Lyra.
A rather non-humorous example from Canterlot Consequences from, surprisingly enough Twilight. Twilight has placed all blame for her fallout with her brother on herself, and none on Shining Armor. When Luna remarks that yes, Twilight should be condemned for losing her temper in the heat of the moment while Shining should be condoned for the same thing, Twilight agrees, having completely missed Luna's sarcasm. Luna and Cadance are forced to be a bit more direct to convince Twilight to stop blaming herself.

Naru-Hina Chronicles: In Chapter 128, Naruto doesn't realize that Minato is so obviously lying when the latter claims that Jiraiya never brought him along when doing some peeping.

In Ships Ahoy!, Olive and Oscar help the Kratt Brothers and Zoboomafoo with a striped scarf preventing visitors from coming to Animal Junction. While attempting to stop the scarf, Oscar accidentally turns Zoboomafoo and every other lemur in existence into a jelly baby using the Candy-inator gadget, and he comes to the horrid realization that since there's no "Unzap All" setting, he and Olive have to go and unzap every lemur themselves. Olive responds with sarcasm that flies over his head.
Olive: [groans] Well, let's fix Zoboomafoo first. I wasn't planning on sleeping tonight, anyhow.
Oscar: Really?
Olive: No, Oscar, that was sarcasm.
Oscar: Oh.

The Power of Friendship (And This Gun I Found!): At one point, Mokuba sarcastically asks Croquet if he's really asking him, the Vice President of the company that makes Duel Monsters, what kids are into these days, while he's being held hostage of the President of their company over a dispute regarding who gets the technology to make even more Duel Monsters. Croquet stares at him before hesitantly guessing/suggesting that maybe kids are into baseball.

Sarcasm Blind / Fan Works