Noticed something about the resident cat the other day…she seems to be left handed. That is, when she walks, she starts with the left front paw. She also reaches for things with that same paw most of the time…
Right now she is sitting on my lap, trying to get me to pet her…by tapping my hand with her left paw.
Curious…
“Animals” covers a lot of critters. Snakes, which are animals, cannot be right-handed, for example. 
Primates can (and are), though.
I’m not sure about felines.
Cats definitely exhibit handedness, or pawedness. When they’re playing with prey or toys, or if you can catch one just as it lunges for a bird. There’s usually a paw that it uses much more than the other. I’ve had a couple of left-pawed cats, although I think right is more common.
Possibly possums and raccoons.
Dogs, too.
With best regards,
Steve Mack
The short answer is “Yes, but . . .”
There’s been quite a bit of work on handedness in animals, and its relation to biological symmetry. Some of the work is still either controversial or inconclusive but:
It appears that there are some species in which handedness is partially sex-based (as in male-female dichotomy; get yer minds out the gutter). Males preferring one hand/paw/claw/whatever, females another.
Some species show a decided preference for a particular “hand” (walruses, for example, are primarily right-flippered, apparently; parrots are primarily “left-footed”, and so on). It’s hard to know what this means, always: do parrots prefer their left foot to hold food because it’s the stronger, more adept foot, or do they prefer to keep a firm grip on their perch with their stronger (right) foot and use the left for the easier task of holding food?
Sometimes species exhibit “handedness” on an individual level. That is, each individual animal seems to prefer one hand over the other, but which hand is preferred isn’t consistent through the species.
Crustaceans are sorta “handed”, in that often one claw is larger than the other, and used for display or crushing.
Some animals don’t seem to display handedness.
Not a single defining answer, apparently. I just think left-handed people are totally bizarre.
And also possibly rats and mice.
This is some kind of veterinary scan of a pet rat’s front paw:
And this is a picture which shows a rat’s hands up close:
Rats use their front paws just like raccoons do…
That rat looks cute.
I know. 
I found the picture on the Internet then downsized it (it used to be HUGE) and hosted it. It shows the little hands well. A rat can pick up a Cheerio with those hands and eat it just like a person might a donut.
I see no reason why those critters with legs (especially the front ones) cannot be either right or left handed. Wings and fins? well, I must say I am stumped there. 
I dunno - Dave - next time you are here, see which paw Wyley whaps you with when you ignore him…
If you see a fish swimming around in circles or a bird flying ditto, then there’s your example of a left-handed/finned/winged or right-handed/finned/winged fish or bird.
The smartest ones probably prefer their left paw/foot/hoof/wing/fin.
Funny. I just did a Google search to see what’s out there on handedness/footedness/flipperness/and so on, and there’s quite a lot!
Right-flippered humpback whales.
Left-footed horses (apparently almost all horses want their riders to mount from the left side). Is this why the horse-racing I’ve seen is done with horses running anti-clockwise, so it’s all left turns?
And so on. Huh. Who knew?
(I like the bit about circling animals, I.B.)
Ha, I don’t care about their handedness. I just wanna know what side the animals come down on the issue of the International Communist Conspiracy!! Harumph.
Or one-legged/finned/etc. etc. As in “Is the Pope a Catholic? Do bears sh*t in the woods? Do one-legged ducks swim in circles?”
That’s one of my favorite rhetorical questions.
Depends. I bet you get one answer from a grizzly, and a rather different one from an ant . . .
And come to think of it, there are all those ants and bees slowly spreading over our borders and across the nation. You right-wingers (ha!) better get that fence built fast.
African Greys are so pretty.