Kindly Vet

While humans have to deal with Dr. Jerk and suffer under the Depraved Dentist, animals are often much luckier. When the beloved Team Pet gets ill or kicked, his owners will waste no time getting him to a veterinarian who will go the extra mile to make sure that your little dog comes out A-okay. When not a Friend to All Living Things, even a vet cast as frightening (usually from the animal's point of view) turns out to be just doing his job. In other times, animals in fiction have this uncanny ability to understand that this human is trying to help them, not that they appreciate getting shots in any case.

Not to be confused with kindly war veterans.

Examples of Kindly Vet include:

Anime and Manga

All the Nurse Joys in the Pokémon anime.
The vet in Azumanga Daioh where Sakaki and Chiyo take the injured cat.
Subverted with Seishiro Sakurazuka in CLAMP's Tokyo Babylon, who is a ruthless assassin under the kindly vet façade.
In Detective Conan, Ran suspects her mother of infidelity and tails her as she meets with a handsome-looking man; Conan deduces that he's a vet and shouts this out moments before Ran opens a can of whoopass on him.
Poor Chi had a dreadful time at her first vet appointment. Didn't help that she had no idea where she was and what to expect (which was having her eyes and ears checked and then having her temperature taken... non-orally), which lead to a short grudge against Mr. Yamada afterwards.
The first season of Magical Girl Lyrical Nanoha had a kindly vet that was willing to treat even strange ferret boys that get sent her way.
Mai Kawasumi of Kanon dreams to become one in the future.

Film

Dr. Dolittle becomes this with the added bonus of being able to talk to the animals. It doesn't always help.
There's a kindly vet in Georgia Rule, too. So kindly, he's the only one who can resist sleeping with Lindsay Lohan. It makes sense in context. Sorta.
The eponymous hero of Corky Romano probably qualifies in personality, although in some cases the pets might have been less fortunate in regard to practice.
Averted in the first Beethoven, with an evil vet as the villain.
In Rise of the Planet of the Apes, Lisa was introduced as a kind vet.

Literature

James Herriot from All Creatures Great and Small. Also in Real Life, as his stories are based in nonfiction. Colleagues Siegfried and Tristan are also as kind as possible to patients.
Taken to the logical extreme in Discworld. Before Dr. Mossy Lawn appeared, your best bet to get cured by a human in Ankh-Morpork was Doughnut Jimmy, a horse doctor. After all, doctors get paid whether or not their patients died. Horse doctors, however, are paid to get results since their patients are thousands of dollars worth of investments whose owners may want to have a word with you in the backalleys if they keeled over under your care.
In Robert A. Heinlein's Have Space Suit—Will Travel, Kip finds himself treated by an alien doctor, rather, alien Kindly Vet, as humans are considered animals by the aliens.
- In his novel Job: A Comedy of Justice, Alexander Hergensheimer's fate is to be decided by a being who is above God and Satan. Alex is rather scared to be brought before this being, so the being kindly uses Alex's memories of bringing his dog to a Kindly Vet, with Alex as the dog.
Dr. Aybolit from the Russian poem Aybolit and its multiple adaptations is the epitome of this trope.

Live Action TV

Kakeru Shishi/Gao Red from Hyakujuu Sentai Gaoranger started out as a veterinarian, and continued to be that way once his day as a Ranger is over. His Power Rangers counterpart, Cole Evans, wasn't one at first, but it is implied that once the series ends, he took up a job as a veterinarian.

Newspaper Comics

Garfield dreads his visits to Liz the vet, usually for no good reason as Liz does her job fine even as Jon hits on her. Recently, Liz finally started dating Jon.
- Liz may be good at her job and treat Garfield kindly, but he still hates being told to lose weight or get shots

Video Games

The Pokémon games have the same Nurse Joys as the anime, but Pokémon Black and White takes it a step further by having doctors and nurses actually standing on some routes and dungeons. What does a doctor do in the middle of a desert with a never-stopping sandstorm? Why, he takes care of people's Mons, of course!

Web Comics

Dr. Winston Thurmad of Freefall, who saves Florence's life during the "Canine in the Water" story arc.

Western Animation

When Santa's Little Helper gets ill, The Simpsons take him to a vet whom they find trying to resuscitate a hamster.
- Which doesn't stop them being a little dubious when he turns up in a later episode as Homer's doctor...
In The Brave Little Toaster sequels, Rob becomes one.
Subverted with Doctor Applecheeks from Tom and Jerry: The Movie, who not only kidnaps animals, tortures them, and sells them for money, but also has a tendency to rape ice cream trucks as well.
The vet in My Little Pony Friendship Is Magic couldn't do anything to help Spike, but she was nice to him.

Real Life

Obviously, James Herriot and any of his competent colleagues.
In a variant, Anthony Guglielmo is a masseuse who developed a sideline giving massage therapy to various animals like penguins, walruses, horses, dolphins etc. Typically, once the animals understand what he is doing to their bodies, they are the first to rush over to this human who makes them feels so good on sight for more.