Paint brushes are made from stiff or soft hairs, which can be either natural hairs or synthetic fibers. Soft brushes are ideal for thin paint which spreads easily, such as watercolor paint, and for detailed work as they can form a sharp point which allows for precision painting. Robust, hard brushes are ideal for pushing around thick paint, and for creating brush marks in the paint, such as when painting in oils using the impasto technique. How you use your brush will, in large part, determine how long it lasts. You want to use your brush for the purpose it was intended.
Modern synthetic brushes are excellent and have the advantage of being cheaper than natural hair. Purists will tell you that no synthetic fiber can beat a Kolinsky sable, considered the ultimate of soft hairs because of its flexibility and strength, which give an artist great control. If you're at all squeamish about or ideologically opposed to the sources of natural hair, then synthetic brushes are the way to go.
Synthetic brushes, man-made of either nylon or polyester filaments treated in various ways, are particularly good for acrylic paint, which can be hard on and damage natural hair brushes, and for large-scale work. In general, brushes made for acrylics can be used for oils and watercolor, but natural hair brushes made for oil and watercolor should not be used for acrylics (particularly expensive sable brushes) unless you are willing to replace them more often. Since you need to keep your brush immersed in water when painting with acrylics, this, along with the chemicals in the paint, can ruin natural fibers quickly.
Synthetic brushes are made to mimic specific natural hair brushes but do not function quite the same - for example, a synthetic brush won't hold as much water as a sable for watercolor. Some manufacturers mix synthetic with the natural hair to make them function more like the natural hair brush.
In general, good synthetic brushes are rugged, maintain their shape well, and can be easily cleaned.
Remember to keep your brushes for oil and acrylic painting separate, although you may use a brush for oil painting that you have previously used for acrylic painting. Once a brush has been used for oil painting, though, it should not be used for acrylic painting.
In a store, a brush usually has a protective coating of starch or gum arabic that helps keep its shape when you first buy it. If you can find one without it, or if the store has samples, run the brush over the back of your hand back and forth a few times to test the springiness of the hairs. They should return to their original shape after each stroke. If not, or there are hairs splayed out, you probably do not want to purchase it. It is common courtesy to avoid testing brushes with your fingers and thumbs, as that leaves dirt and oils on the brush from your hands.
The higher priced brushes are generally the higher quality brushes.
Once you get your brush home there are many other things you can do to test the quality of the brush. Read this thorough article on how to test watercolor brushes.
It is important to care for your brushes properly to avoid ruining the bristles. This means cleaning them well after using them and storing them properly so that the brushes are in good shape to give you the painting effects you want the next time you are ready to use them.