By “save” I mean theoretically (since the impact of one person on the overall meat market is neglible) reducing the demand on meat enough to save an animal.
Only the individual can answer this for him/herself. So, how many animals do you eat? 
If you count one animal for every time you eat some of that animal, the number would be too inflated. Eating an 8 oz. filet mignon obviously doesn’t count as one whole cow. We need some stats here - how much usable meat do we get from your average head of cattle, pig, lamb, chicken, etc.
I’ll roughly estimate that I eat the equivalent of 1 chicken every week, one cow every year, and one pig every 2 months. So if I live another 50 years, and turn vegan today, I will have ‘saved’ 2600 chickens, 50 cows, and 300 pigs.
Of course, the other way to go about this would be to add up all the animals slaughtered in the US in a year and divide by 280 million. Or divide by less, if you have an accurate count of vegan/vegetarians, but I’m guessing they’re considerably less than 1% - 2.8 million vegetarians sounds high to me.
I think that would only be a first-order approximation, though, as it only accounts for direct mortality due to eating the poor buggers. What about all the collateral damage from farming methods, oil spills, pesticides, rodenticides, roadkill, habitat change, etc.? You could assume that these are constant; i.e. that the impact of your life in these ways does not depend on your diet, but that would be an assumption. Note that I have no idea whether the assumption is valid, or how to check it, but it’s an issue to consider…
You don’t save any! Animals are raised for slaughter - they’d just raise fewer of them. It’s not like they’d raise them to live to old age in a pasture. If it’s better to live a short while in captivity than not at all, then you should eat more animals to do them a favor.
Except, fish (most of which are caught from the wild) and any animals you hunt or get from hunters.
None, if they get all preachy and sanctimonious about their new vegan-hood and prompt the people around them to eat more meat out of spite.
Nature is this big rich tapestry of intertwining effects, y’see…
If everyone in the world suddenly went vegen, wouldn’t cattle and chickens and so on effectively become extinct? I mean, there are breeds of wild cows and chickens I guess, but in enough numbers to keep the species going?
Napler is correct here. But, if instead of going vegan you only become vegitarian, and so still eat milk products you would move some farm animal number from being bred for slaughter, to being bred for milk. Then if you insisted on only buying ‘humanely’ produced milk products, and lots of them, you might actually improve the life for a few animals.
That’s quite a substantial appetite. A market weight feeder will dress out at 600-700lbs. A market weight hog will dress out at about 150lbs. And chickens are usually slaughtered at roughly 3lbs. So you’re proposing to eat 2lbs of beef, 2.5lbs of pork, and .5lbs of chicken every day.
You really have to look at the larger picture to get any kind of answer. Farmers make their decisions based on profit margins. Let’s say you are extremely persuasive, and you manage to take 50,000 other people with you in your switch to the vegan side. If they all live in your town, there will be a big influence on the restaurants and grocery stores. They’ll change their buying patterns, and cater to the suddenly less meaty community. Overall, though, the farmer can still sell pigs, steers, and chickens. Your vegan troop probably won’t make even a penny-a-pound difference in the price of meat. At that rate, the farmer may grumble, but he won’t stop selling pigs as long he’s making money. The weather makes bigger differences in his profit than you ever will. Meat-eaters won’t even high-five you for making their pork chops cheaper.
If you want to go vegan, do it for yourself. You won’t really save ANY animals.
viking is quite correct that you need to look at the whole picture. Almost all vegan food is produced by intensive agriculture, That means cutting down the forests, scraping out all the herb layer with a tractor and then planting amonoculture. That monoculture then has to be protected with fences, scare devices or poisons that effectivel mean that any animal that was living on that patch of land starves or is skilled. It is possible to reduce this somewhat by adopting ‘organic’ practices with no pesticide usage, but that is not practical for feeding everyone, so it become a decision you can only apply to yourself is you want to avoid killing millions of animals a year as a vegan.
In contrast most meat is raised free range for at least part of its life, and it is still possible to buy entirely free range meat. Over large parts of the country free range meat is produced in areas that once supported antelope and buffalo. No massive landscape change as occured and only a few animals have starved to death. Even fewer are killed for every animal raised. Again, it becomes a personal choice whether you want to eat only free range meat.
So it becomes a 4-way decision between killing a few thousand catterpillars, rats and crows every year as a vegan or killing a few a few thousand catterpillars, rats and crows and sheep and cattle every year eating normally, or killing a few hundred catterpillars, rats and crows each year eating organic vegan food or else killing a few dozen cattle sheep and lice every year eating only free range beef.
In the final analysis if your sole interest is minimising animal deaths from the production of your food you would go on an Atkins diet with free range meat and enough organic vegetables to keep you healthy. Going vegan will result in the deaths of more animals. Of course most people don’t eat only free range meat, but then most vegans don’t eat only organic food.
There isn’t a simple split betwen vegan and normal on this question, it’s a split between normal diets and three alternatives, of which an Atkins style diet saves more animal lives than vegan.
Napier is correct here as far as domestic animals. If animals are not eaten, they are not sold. No one raises animals that no one wants to eat.
Going vegen prevents animals from living. It doesnt cause any to be “saved”. It only prevents life from occurring in the first place. If we all ate a million less cows, our ranchers would raise a million less cows.
As far as wild animals, again no change. The total number of wild animals out there and how many die each year is mostly a function of their habitat, and how many animals their wild lands can support.
Again, not hunting and the not eating of wild animals will still not save a single one of them. The number of animals that die each year, will be the same, whether they die by bullet or starvation, disease, or predators.
Oops.
See, I told you I needed someone to come by with stats.
You could probably “save” more animals by deciding that you would never again eat in a restaurant or use ice. Environmental impact and all that.
Thanks for doing this, since it seemed a bit exaggerated to me. In particular, I was thinking that Jake4 sure likes his bacon and/or sausage at breakfast time. 
(Tries to envision people eating more beef out of spite. Fails. Runs screaming from thread…)
Since this is GQ, I’ll ask j.c. what reason he/she has for saying avoiding resteraunts would “save” more animals?
Is it just that resteraunts waste more food, than is wasted with home made food?
Actually, no; the breed of cow you eat is not the same as the breed of cow you milk. Likewise, layer and fryer chickens (at least the mass-produced ones) aren’t the same critters… though I believe some of the boys of the layers’ broods get cooked, so maybe you could save some future roosters that way. This would present a problem, as many of the vegetarians I know specifically avoid fertilized eggs… I’m visualizing a new market for production-line but humane rooster vasectomies…
Modern commercial-scale “farm animals” are intensively bred to give high yields only in their target use.
Actually, raising “dairy beef” is one option that some dairy farmers use to diversify their operations and also use the male calves that are a byproduct of the dairy production process (the female calves are usually raised as milkers).
However, there is a significant amount of consumer resistance to the concept (actually the resistance is at the processor level – the consumer probably could give a rat’s ass).
Not so long ago, the great dalmuti (I believe) started a thread in GD (which I’m having trouble finding, for some reason) that asked what meat-eating humans were thinking while they ate? It was posed as an innocent question, but it was fairly obvious what he really wanted was for meat-eating humans to feel guilty and ashamed and start getting defensive about our eating habits. Naturally enough, this board is full of people too smart to fall for a blatant stunt like that, so in addition to people responding that meat-eating simply wasn’t a moral issue at all to them, a few wiseguys replied “I’m thinking ‘Hmmm, good meat’” or “Needs salt!” or “Ha ha! Stupid chicken!”
Because dalmuti’s stance was sanctimonious (not to mention intentionally trying to be deceiptful), the responses largely took the offense, not the defense, and I expect a few posters who previously hadn’t had specific dinner plans before reading the thread, deliberately chose steak, hamburgers and chicken etc. that night.