Barbed wire is one of the most common types of fence, and it will keep in large animals such as horses and cows with no trouble. Barbed wire is typically attached to metal T-posts or wooden posts, with four or five strands, depending on how secure you need it to be.
Woven wire is ideal for smaller animals, such as pigs, goats and sheep. It is made up of wire that is woven into squares too small for these types of animals to fit through. You can top it with a strand of barbed wire to help keep jumpers in, or use it as-is.
Electric wire is a very economical way of fencing in animals, and most can be trained to respect an electric fence. This type of fencing works best on interior cross fences, but can also be used as a perimeter fence with enough strands.
Livestock panels are more expensive, but consist of galvanized metal welded together to make a solid, moveable panel. These will keep almost any critter fenced in, and can be easily installed on any area that is flat.
Whatever fence you choose, make sure it will hold the types of animals you have now and any you plan on getting in the future. It is much easier to build it once and be done than to have to change it as your needs change, so plan ahead and save yourself a hassle in the future.