Ears as Hair

Bugs: I like your hair.

Lola: Thanks, heh. They're my ears.

—The Looney Tunes Show

Lots of media stars Funny Animals, and as we all know, some animals have rather long ears, such as rabbits and various breeds of dogs. In nature, these ears serve the purpose of enhancing hearing, but once you put an animal on two legs, the ears serve a different purpose. Very often, Funny Animal characters will treat their long ears as if they were hair. Braiding a real animal's ears would hurt immensely, but Funny Animals seem to have no problem with it.

Examples of Ears as Hair include:

Anime & Manga

Inverted in Shitsurakuen: Tomoko Oashi has hair which, according to the main character (Sora Himoto), looks like ears.
Usavich: Putin has his ears tied in a top-knot.
Rosario + Vampire: Nekonome-sensei's cat ears blend in with her hair, making it look like it's simply another layer of feathered hair.

Comic Books

Usagi Yojimbo: The hero, Miyamoto Usagi, most often has his ears pulled into a ponytail, or possibly a top-knot. When he puts on a hat or a helmet, they disappear completely.
Star Wars: Female Gungans often tie their ears back.

Films -- Animation

Disney's Dumbo. Before he tries to participate in the pachyderm pyramid trick, Dumbo's ears are tied above his head so he won't stumble on them. Guess what happens while he's running out to the spring board.
In Who Framed Roger Rabbit?, Roger wrings water out of his ears. And yet it hurts him when Eddie picks him up by the ears, because he does not think it's funny.
Bugs Bunny's Distaff Counterpart from Space Jam, Lola Bunny, ties her ears into a ponytail, as seen in the page pic.
Lady from Lady and the Tramp often poses with her ears arranged like hair, or flips her ears back like a shampoo commercial, giving the appearance of long flowing locks.
Sasha from All Dogs Go to Heaven 2 has the same type of ears as Lady-and treats them the same way, even flicking one of them behind her head with a casual paw swipe, with them sometimes dipping in front of her eyes, particularly when she's being sultry.
Dixie from The Fox and The Hound 2 also has the same kind of ears-seems to be a thing with Disney dog females-and treats them the same way, even wearing a black bow in a way that should be physically impossible.
Maid Marian from Robin Hood is actually depicted wearing an outfit that includes a hat shaped like her ears.

Films -- Live-Action

The Togrutas and Twileks from Star Wars. Arguably the Twileks' things are rather some sort of head-tentacle-thing...trope still counts, though.
- Togruta actually have the same kind of headtentacles as the Twi'leks, though they don't seem to have the same fascination with 'styling' them as the Twi'leks do.

Video Games

Cream the Rabbit from Sonic the Hedgehog has her ears as sort of the equivalent of Girlish Pigtails.
Klonoa's ears wave like hair when running.
The Usuls from Neopets appear to have scrunchies holding up their ears, though Hannah from the games "Pirate Caves", "Ice Caves", and "Kreludor Caves" is depicted with human hair on her head.
- Delma Harrence, defender for Faerieland's team in the Altador Cup has a hairband around her ears, and because they flop to the side, they essentially look like a side-ponytail.
Inverted with Juri from Street Fighter IV, whose hair has been compared to cat ears/ox horns. In one of her concept designs, the two parts of her hair that stick up were less pronounced, and genuinely looked like cat ears were a part of her hair.
Inverted by Toyosatomimi no Miko of Touhou 13: Ten Desires, a newly-resurrected saint whose hairstyle resembles animal ears (hence the name). Her actual ears are covered by giant earmuffs, further confusing the issue.
Fay Spaniel from the infamous unreleased SNES game Star Fox 2 has shaggy ears that REALLY look like hair.

Webcomics

Furry Experience
- Ronnie (again, a rabbit) usually has her ears looking like wavy hair, though she braided them at one point. At another, she had to worry about a "bad ear day" and a "bad fur day" at the same time.
- Her roomate, Dawn Doe, wears her ears down, in keeping with her more formal dress style. They only point upwards when she's surprised.
Big Ears from Goblins usually ties his namesake ears back in combat situations.
Cupcake from Sugar Bits, has both real hair and this trope as part of her hairstyle.

Western Animation

Loonatics Unleashed: Lexi ties her ears up in a ribbon. Given who her ancestor is...
Babs Bunny of Tiny Toon Adventures: "Do you like my ears better up or down?"
Dot Warner from Animaniacs wears her ears in a scrunchie.
The Better Bottoms rabbit from CatDog wears his in a sleazy ponytail style.
Parodied on Family Guy with Peter's line about Brian's appearance at an upcoming dog show: "We haven't even talked about how you're gonna wear your ears. You know, 'cause I was thinking up."
Usagi Yojimbo (see above under Comics) is also a semi-regular character on the Teenage Mutant Ninja Turtles.
Lola Bunny also occasionally does it in The Looney Tunes Show.
Subverted in Team Umizoomi. Milli is a girl, but what appear to be ponytails coming out of her hat are actually tape measures.
Molly Cunningham on Tale Spin wears hair ribbons around her ears.