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.
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.
Fish from The Boxtrolls. Despite being a shy, cowardly creature, it's evident Eggs is more important to him than anything - and he proves it, too, even lashing out at his attackers when the boy is harmed. He's knocked out almost immediately, but considering the boxtrolls' nature, it was a brave act.
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.
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.
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.
Dr. Nefario becomes one in the sequel. When El Macho tries to take over the world with an army of Brainwashed and Crazy Minions, the good doctor, who helped him with the plan, develops an antidote when the villain decides to attack Margo, Edith, and Agnes. A quote after the fact sums up this trope:
Dr. Nefario I mean, I'm happy with creating an evil army to destroy the world...but nobody messes with my family.
In Epic, Mandrake singlehandedly destroys an entire tree after someone makes light of his son's death.
For clarification Mandrake is two inches tall and the tree is around 30 feet.
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.
Mumble from Happy Feet goes beserk if you try to harm his son. If you are a skua who tries to harm his son, he will bash you aside as if you're a bowling pin. Even if your an elephant seal, HE!WILL!RAM YOU!
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.
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.
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 the monkeys outright, "Keep your flea pickin' hands 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".
Tramp from Lady and the Tramp fights and kills a rat in order to protect the infant son of Lady's owners.
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...).
Spike is a literal example in the Rugrats films. In the first film, he fended off a wolf that threatened the babies. In the crossover film with The Wild Thornberrys, he teamed up with Eliza to find the babies.