Well, for cows, I knocked on the farmer’s door and told them their cows were loose. 
I never had to round help them up, but holding your arms out and talking was what the farmers used.
For bulls, I use my 0th Rule for Right of Way: the bigger guy wins.
Well, that explains a lot.
Last time I had this problem I yelled, “I’m a big pink bear and I’m going to eat you for breakfast!” while waving my arms. Of course, the animal in question was a black bear, and the poor thing immediately turned around and ran away in terror. It’s a good thing that bears don’t have mirrors because if they did they’d realize that I’m no match for even the smallest mature bear.
Stranger
I use the kitty move sound, named by my husband when I accidentally used it on him and he exclaimed, “did you really just use the kitty move sound on me?”
It’s sort of a staccato whispery whistle/hiss. It’s usually used on my cats when I wish them to get out of my way, but it works on unwanted outside animals too. It also works on children (and sometimes husbands…if they’re not paying attention).
I grew up in Iowa.
My dad says something that sounds like “Ous-get-outs” and I’ve caught myself saying that to my dog. We are both from the midwest.
Most often, though, I say “Beat it!”
Usually I’ll say, “Shoo!”
There are other things I’ll say, though: “You know, this is foolish. I don’t like cats. I live in a no pets building. And I’m not going feed you. If you keep insisting on following me I’m going to call Animal Control and turn you over to them. And I won’t shed a tear to think that’s probably going to get you euthanized. You really ought to buzz off.”
They don’t seem to understand that, though. It might have something to with the pleasant, thoughtful tone.
(That, and in general, I only seem to scare random people, not random animals.)
I did some door to door work once, and had heard that one way to calm an angry guard dog was to kneel down to as if to pick up rock. A few days later, I walked past a house with a chained dog who was kicking up a fuss at me. I decided to give it a try and before my hand even touched the ground, the dog had stopped barking. I guess it only works if the animal has had things thrown at it in the past, but it sure worked that time. There was no rock on the ground, but I remained calm and stared at the dog like I had every intention of arming myself with a rock or stick. I just did it to see if the technique had merit, and I felt bad for the dog as he obviously had seen this from humans before.
If the animal isn’t a physical threat I just say what Jeff Foxworthy’s dad says: “gi-on-outta-heah!”. Clapping helps too.
My last encounter with an unwanted dog was at a friend’s kegger. He tried everything to get the dog to scram, but the mutt wouldn’t take the hint. By 3:00 AM, my friend was passed out in the laundry room next to the dog. Good party.
I use any phrase I wish to use, and, with some of the animals I have dealt with, that can run into a long list of phrases before they get the hint.
My gun says, “BANG!”
I’m kidding, of course. I use an air rifle.
Yep, for nonthreatening animals and children.
For threatening animals, I say “kennel!” Seems to be effective for dogs and young, drunk moose. Pissed off skunks, not so much. 
I grew up in Colorado
I have a ‘sheepdog voice.’ I grew up on a cattle station (ranch to you Americano folk) and at a young age, developed a way of yelling which is about two octaves deeper than my speaking voice and very harsh and gravelly. Even now, 25 years after leaving the station, if I see a cat/dog/horse/cow in the wrong place, I immediately switch into it. People that have never heard it before are rather shocked that I sound like a cattleman when I’m a little girly girl. Hee.
My usual sentence goes a bit like “GGGet… OUTofit”
One of our cats is absolutely attached to my computer chair. She’s almost always there when I want to sit down. Most of the time, I say, “Move!” Sometimes I’ll do “Git!” Occasionally it descends into words for which one only sees the polite analogues in print…
I bark and jump at them, actually. It’s more effective.
“Kishta!”
Why, I have no idea. The word has no meaning I can discern. It’s just what we say around here.
The only unwanted animal I have to deal with is Canada Geese. They hog (and crap all over) the path where I run.
They’re impervious to noise of any kind, so what you say makes no difference. But, I’ve discovered that if I extend and wave my arms, it activates their instinctive fear of raptors, and they clear out. I feel like God when I do this.
Usually it’s “Git!” followed by the ritual Brandishing of the Garden Implement. If that’s insufficient, they receive Inarticulate Roaring accompanied by Pursuit to the Property Line with Intent to Do Bodily Injury.
There are feral dogs around here and I have to chase them off. Tater and CrazyHound are neighbor dogs and are OK. Tater’ll go home if I tell her to, but I don’t usually bother. CrazyHound is, well, crazy…she just wanders all over creation, howling. Everything else flees the moment they see me.
Oh, and I run off rabbits without a word. Just chase’em over the property line and let Tater pick up the pursuit.
First I offer them a copy of WatchTower.
If that fails, I see if they are interested into an exciting money making opportunity.
I think I like your method the best. And hey, If that doesn’t work Tater will take care of it.
Something like PPPRRRSSHHHTTT. Just to startle them and seem vaguely threatening.
Isn’t “kishta” Arabic for cream?
“Oi!” seems to work well on most domestic animals, as well as humans from all over the world.
Cats and small dogs that are on smooth flooring where I need to stand will also be swept aside with a foot. Large dogs attempting to knock me over with joy are usually hip-checked back to the floor. Strangely, humans don’t tend to stay long enough to be an obstruction once I’ve shouted at them…
Another phrase all the dogs in my parents’ house know is, “Don’t help me!” Tragically this seems to have been invented too late for Mom to use on us girls as little kids.