One Piece has Chopper, who doesn't have stubs for hands, but does have reindeer hooves. And while he can shapeshift into forms with hands, he prefers to do the majority of his medical work with his less-dexterous hooves. The author has made some attempt at explanation◊, but he shouldn't have human-levels of manipulation with his hooves like he seems to.
Pucca doesn't have fingers, neither does anyone in Sooga. This was lampshaded when a character wanted to call on a phone but couldn't dial, when she asked how this works, the others only look at their own hands and answer "I don't know."
Most BIONICLE characters prior to the '09 line of sets (which first introduced an original hand-piece) manipulated things with their unmoving "hands" in animation, if you can even call those pieces they had hands. Clenched fists, open palms, pointing finger — these were all accomplished by the same inarticulate LEGO piece. Even if a character had fingers, some animations still depicted objects simply sticking to their palms. Averted in the Direct-to-Video movies, in which they were given five, at times four-fingered hands. Strangely played straight in a scene from the first movie, however, when Takua uses a never-before seen magnetic force to pull a wooden staff to his palm. In fact Word of God claimed that when we don't see the characters using fingers, they utilize their magnetic abilities (also used for keeping their masks on their faces and backpacks on their backs, no matter what material they're made of).
Kirby is able to wield swords, hammers, and umbrellas among other weaponry with his stubby little arms. The official art of Kirby And The Amazing Mirror does show his arms wrapped around objects and his cell phone only having two buttons, making it slightly more believable but in the game itself objects just hang on the end of his arms.
Workers in Globulation, as the name implies, consist of a handful of blobs, but manage to cut trees, chip stone and make a lot of stuff up to what seems to be steam cannons.
Several Pokémon, but notably Jigglypuff, who in the anime was able to hold and pull the cap off of a marker to draw on people's and Pokemon's faces after they fell asleep listening to its song. All with the lack of fingers.
In Minecraft, the player's hand is a solid cube, yet able to hold and use items. (Although, if playing in first person, items float infront of you)
All Chao, as well as Knuckles, who has mitten hands.
Some Mario enemies like Shy Guys and Boos lack hands, but still grip their equipment just fine in the Mario Sports games. When someone asked Nintendo Power how this worked, they said that when they asked them how they gripped their tennis rackets in Mario Tennis, Shy Guy said something about a complex series of magnets while Boo just muttered something about "sticky ectoplasm".
Basically every single character in Animal Crossing. The human Player Character is portrayed without fingers, but still manages to do anything a normal human can do. And more obviously, all of the animal villagers can also do every mundane activity without trouble. How can a bird villager write with their wings? How can a deer villager use a fishing rod with their hooves? How can a cat villager use a bug-catching net with their paws? Smug-type villagers in New Leaf will even mention being able to play the acoustic guitar, even though they're a mouse, or koala, or horse, or...
Characters in Fruit Incest don't seem to have fingers or toes for the most part. They will occasionally gain a finger or two for the sake of pointing, but any fingers not being currently used will simply appear as one giant mitten hand.
In Happy Tree Friends, every character except Lumpy has only thumbs, but still shows fine motor control, such as clenching objects and manipulating small devices.
They can grow fingers at certain times, just not all the time. "We're Scrooged" anyone?
Handy loses this ability when he's on screen (what with having amputated arms).
Did no-one else think it was weird for the character in image 110 to wearing a sling when he only has free-floating circular hands?
Everyone from Retarded Animal Babies. This is actually lampshaded in the Thanksgiving episode where Puppy actually forces Bunny to punch a turkey with brass knuckles, but Bunny cannot put them on because he has no fingers. Puppy then proceeds to cut up Bunny's hands so that he now has "fingers."
Lampshaded in an episode in which the Powerpuff Girls end up switching bodies with Professor Utonium, Miss Bellum and the Mayor, leading to Buttercup having trouble using Prof. Utonium's hands. She just kind of waves it around behind the phone, without moving the fingers at all.
My Little Pony: Friendship Is Magic has this, despite producer Lauren Faust apparently placing clear orders against their use. Although most of the time ponies use their mouths or magic to manipulate objects, there are cases where they grab things with their hooves. This is normally a script issue, one storyboard artist relating a tale of a script requiring a character to use a pointer and speak at the same time. Every once in a while they'll come up with a clever aversion though (such as an umbrella that is connected to a saddle rather than having to be held).
The older My Little Pony Tales series had them use their hooves as hands almost exclusively, with no difficulties, no explanations, and no lampshading.
Sponge Bob Square Pants: Patrick Star and picks up and manipulates objects despite being a starfish with no appendages.
As does Plankton.
Winnie-the-Pooh, Piglet, and Tigger have thumbless, fingerless hands like that of The Powerpuff Girls. Pooh and Tigger also have thumbs that appear only when grasping something or gesturing. Justified in that they're stuffed animals.
The clay characters in Gumby, such as the title character, have fingerless hands. Justified in that they're made of clay.
The characters in The Large Family, similar to the MLP franchise, in that they can hold objects without any problems whatsoever.
Babar's been doing that long before The Large Family came around. Despite many times they use their trunks to hold things, they tend to carry things on their hooves. Notably in "Babar:The Movie" Arthur is seen balancing a bowl of cereal on one hand, and in the sequel series Babar:The Adventures Of Badou one scene shows a few of the castle staff letting loose and playing electric guitars (Not with their trunks)
Dolly from Toy Story 3 has thumbless hands like The Powerpuff Girls, but she has two lines of stitching on each hand that indicate fingers. Justified in that she is a ragdoll.
Purple pony:(hanging onto the other pony's hoof with both of her hooves) Hold on to me, Guillermo! Guillermo: I can't! I don't got no thumbs! (the purple pony loses her grip and falls into the volcano) Purple pony: Ahhhhhhhh!!!!