In 101 Dalmatians, Pongo teams up with Perdy to lay the hurting on the two thugs about to kill not only their puppies but all 99 puppies. Their treatment of the bad guys is SCARY. You do not mess with puppies and let their parents find out.
Gru from Despicable Metakes a level in badass after his three adopted daughters are kidnapped. Among other things, he hopscotches over a group of heat-seeking missiles fired towards him and one-punches a shark!
In a minor case, when the carnival barker denies Agnes the unicorn she wanted, even when she hit the nearly impossible target. He almost makes her cry, and Gru shows him why he should never mess with the adopted children of a supervillain.
Whether it's Disney's The Jungle Book or TaleSpin, messing with Mowgli/Kit will get you trouble from Baloo. In the former, he tells Big Bad Shere Khan outright, "Keep your flea-bitten paws offa my cub!" In the latter, discovering that someone has conned Kit leads to a different threat, "Wait until I get through with that guy he'll be able to count his teeth on one finger!" Both Mowgli and Kit even affectionately call him "Papa Bear".
Hiccup is lucky enough to have two of these...one is his biological father, a Bad Ass Viking who's willing to punch dragons in the face and dent metal with his hammer to protect his boy, and the other is a freaking dragon. A dragon who attacks and drives off another dragon a little over three times his own size when the other threatens Hiccup.
The Lion King: Mufasa is the best father ever (no matter his species), as he is wise, just, loving, stern when necessary, and royal. But don't you dare cause any harm to his kid, or he will find you and he will kick your ass(unless you're unlucky...).
Although not the biological father, O'Malley from The Aristocats adores Duchess and her three kittens, and he fights quite ferociously to prevent the Big Bad from shipping them to Timbuktu.
Marlin in Finding Nemo, because how many fish do you know would risk life and death across an ocean that is infamous for some of the most POISONOUS and DANGEROUSLY VICIOUS creatures of the sea, to find his son? He's not even a shark, he's a clownfish who's scared of everything.
When Syndrome kidnaps Jack Jack at the end of the movie, Bob throws a freakin' car at him.
The look Bob gives Syndrome when he is told his family is dead sums up this trope.
As does the moment when (still thinking they're dead) he nearly strangles Mirage, and threatens to break her in half.
Fergus in Brave is a loving husband and father who would fiercely protect his wife Elinor and their four children from any danger. However this almost has some serious consequences when he goes after a bear because he thinks the bear has killed Elinor and is now attacking their daughter Merida. The bear actually is Elinor, who has lost control of her bear form and has lapsed into wild behavior, but Fergus is mad with grief and refuses to listen to Merida's (admittedly crazy-sounding) explanation.
Wreck-It Ralph is a nine foot tall, 643 pound Gentle Giant. Harming anyone he cares about, namely Vanellope, will bring out the worst in him.
"Hey! LEAVE HER ALONE!"
The Croods: It doesn't matter if you're a weird cat/owl hybrid thing, and multicolored sabertooth cat or even a new and more civilized cave person. If you threaten Grug's family, indirectly or not, he will take you down.
Tramp from Lady and the Tramp fights and kills a rat in order to protect the infant son of Lady's owners.
In Epic, Mandrake singlehandedly destroys an entire tree after someone makes light of his son's death.
Spike is a literal example in the Western Animation/Rugrats films. In the first film, he fended off a wolf that threatened the babies. In the the crossover film with The Wild Thornberrys, he teamed up with Eliza to find the babies.