Could be animals, robots, animated characters, just as long as it/they is/are not human.
If it’s not obvious this is mainly for laughs.
I am Groot.
Robbie
M-5
Deep Thought
A monolith
I’ve been fascinated by this bird since I was in grammar school.
First appears at 0:04 and then throughout.
Some YouTube appearances call it a Mynah, but it looks too much like Heckle and Jeckle to me. Anyway, I used to try to walk and hop like that. 
I always thought the mother dog in *Babe *deserved an Oscar. Watch the scene where the puppies are being given away and tell me you haven’t seen Best Actress awards for far less.
That was great.
Also, Buddy, the dog who played Comet on Full House also played the title character of Air Bud.
But no thread can be complete without a mention of Moose, who played Eddie on Frasier. Oh, that stare.
Bart the Bear, of course.
HAL is a close second.
The title character in the French film The Red Balloon. Such a masterful, expressive performance.
Are Tom Servo and Crow movie stars? Because they’re right up there.
Dory, the ditzy blue fish in Finding Nemo.
Zira and Cornelius in Planet of the Apes.
Chance, Sassy, and Shadow in Homeward Bound, The Incredible Journey.
Babe, the pig. (All the animals, of course, but honorable mention to
the duck in the movie, who looks more like the handle of an umbrella than a real duck, but never mind!)
Do puppets count? If so, then Crow T. Robot & Tom Servo … Gypsy too!
Tie between:
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Bruce, the shark from Jaws
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Otto, the inflatable auto-pilot from Airplane!
Good one. I’ll nominate the gals from Jurassic Park.
Crap–you said movie stars. I better withdraw Moose. 
Though apparently he did take the title role in My Dog Skip.
I don’t know his name (SAG rules regarding credits were much more relaxed in those days), but whoever played the lead canine in the old Warner Brothers shorts in the '40s was brilliant. He had great range; could play a wolf or a coyote. There were some makeup tricks involved, but mostly he conveyed the difference with subtle changes in mannerisms. He could be the articulate, erudite foil when teamed with Bugs Bunny. But he really achieved his greatest triumphs as the tragicomic mute hero alongside the Road Runner. He could convey the whole range of emotions, frustration, inconvenience, irritation, peevishness, with nothing more than a raised eyebrow and small sign.
That guy was a genius.
HAL 9000
Alien
Predator
Old Yeller
Old Dollar, for hauling John Wayne’s fat ass around
The horse in Cat Ballou
Rin Tin Tin
Sgt. Preston’s faithful lead dog, King
Silver
Trigger
Scout
The official name is “The Minah Bird,” and he’s nothing like Heckle and Jeckle (who came six years later). He was created by the great Chuck Jones in a series of five cartoons, which are hard to find today, since the main character of them was Inki, a stereotyped African native. Inki isn’t a particularly demeaning character in his actions – at worst, he acts like an inexperienced kid (which is what he is) – but his character design matches the most offensive stereotypes of Aficans.
But the Mynah Bird is one of Jones’s greatest creations. He was enigmatic, unfathomable, and did nothing but walk across the screen (to Mendelssohn’s Hebrides Overture) – but he was an unstoppable force of nature if you got in his way. Supposedly, Walt Disney took one of the Inki cartoons, showed it to his cartoonists and demanded to know what the hell was going on in them.
He is one of my favorites, too.
Rin Tin Tin
Mighty Joe Young
Son of Godzilla
Paul
Rango
Zunar-J-5/9 Doric-4-7 also known as “Jake” (from The Cat From Outer Space.)
Benji
The aliens in Agent K’s locker in Men in Black
Robbie the Robot
The Rapist Robots in Flesh Gordon. (if you want to google it, make sure you get a video clip. Still photos are just not as funny.)
He doesn’t have a lot of fans, but I’ve always liked C-3PO.
And Wall-E.