There are, as of the 1.2 patch in Minecraft, six animals that can be bred, of which only four can really be kept in pens.
The animals that are easily kept in pens are: Pigs, sheeps, chickens, and cows.
Pigs are unfortunately the least useful animals in the game. The only resource you ever get from a pig is pork- which, admittedly, is the second-best meat to have in the game for keeping your hunger bar full. Still, it’s not -that- much better than chicken, and pigs don’t give you anything else at all. Frankly, if you can find any other herdable animal to keep, don’t worry about keeping pigs. Generally, I kill them when I come across them if I need food and simply don’t worry about depopulating them.
Sheep are much more useful animals to have around in Minecraft. This is because of wool. Killing a sheep will yield one block of wool- two if you are lucky. Shearing a sheep with the Shears tool, however, will give you two to three blocks of wool. And since sheep consume the grass that grows atop dirt blocks (and grows back regularly) to replenish their wool after you shear them, this makes them an effectively infinite source of blocks. Especially since applying dye directly to a sheep will permanently change its wool color, giving you an infinite supply of colored blocks. Aside from being an awesomely colorful building tool, wool blocks can be used to make the string needed for bows and fishing rods, and on top of that are needed to make the bed. As the bed is the only built-in way to change your spawn point, this makes wool just a little bit important.
Chickens are also quite useful- as they provide both chicken meat and feathers. Feathers are mostly just used to fletch arrows, but as anyone who’s used the bow and arrow can attest, being able to shoot mobs from a distance is hugely important, especially if you intend to ever kill a spider jockey. Chicken meat isn’t terrific (the only worse meat for your hunger bar is fish), but it is still a food, and chickens are -really- easy to multiply. This is because they not only can be bred like other animals, they also periodically lay eggs, which can be thrown for a random chance of spawning a baby chicken. This makes chickens almost as much of an infinite feather/meat resource as sheep are an infinite wool resource.
Cows produce three different resources, though two of them are of relatively questionable importance in most cases. When killed, a cow will drop 0-2 beef and a similarly randomized number of pieces of leather. Leather is used to make the lightest, most basic armor in the game, so it’s not that great of a resource, but it will let you armor yourself if you can’t afford to spare the iron or diamonds to keep yourself protected all the time. If you have a bucket, you can use it to collect milk from cows. This would probably be more useful if milk was a healing item- instead, milk will cure poisoning and disease. As poisoning is infrequent and disease only happens when you eat zombie meat or uncooked chicken meat, this is not terribly useful, especially since milk, being collected in a bucket, cannot exist in stacks in your inventory. This is okay, though, because milk is needed to make the Cake- and beef is the best food in the game short of the cake, and far more portable than the confection is.
The other two kinds of animals you can keep are cats and dogs- and neither of those is really a herd animal, so I’ll leave those for later.
Now, this tells you why you would want those animals- but how do you get them?
Well, there’s a reason that this is Journeyman farming and growing plants is Novice farming. In Novice Farming, I explained how to grow plants- including wheat. Harvested wheat, the bundles of it, is the way to get these animals entrapped. As long as you are holding a bundle of wheat in your hand, any pig, sheep, chicken, or cow that can see you will follow you- given a chance to keep up. Remember that the only thing in the game you should have encountered that travels as fast as you do is the Enderman (which travels faster). This means that it is easy to outpace an animal that you were hoping to herd to your animal pens and keep.
Curiously, wheat is also how you breed animals- if you right-click an animal with a bunch of wheat, hearts will appear over it’s head- and it will, instead of following you, head for the nearest other heart-struck animal of the same kind. When two heart-struck animals meet, they will run against each other for a moment, and then produce a big-headed tiny baby animal of the same kind.
I believe that covers wheat and animals, so it’s time to move on!