There are a lot of brands out there on the market right now. Choosing which one you prefer truly requires you to go to an archery store and shoot them. From personal experience I have preferred Hoyt or Mathews. They are a leaders R&D with having designed the first carbon fiber bow for commercial sale. Their quality is exquisite and they have good warranties. Mathews who is the largest bow company in the world is also a good choice if you are looking to buy a quality bow that will last you a long time. A new company that just recently opened called Prime has invented a new quad cam system in which each limb has 2 cams minimizing the torque of the string and allowing for an extremely smooth release. If you are looking for a relatively inexpensive bow than I would recommend going with a Bear or Martin. They are a little heavier than bows made by Hoyt or Mathews but do well if just entering the archery scene. Here is a comparison between 2 companies and how different their products are.
 
Here is a bow made by PSE. If look at the limbs you can tell there is a sharp curve to them. This is a particular trait associated with their craftsmanship. Another quality that sets them apart is the shape of their cams. most cams have gradual curves to them. PSE on the other hand has a much more aggressive system on their bows which allows for a faster arrow speed but not nearly as smooth of shot.

Here is an example of a bow made by Hoyt. As you may notice it has an interesting handle design. this is because it is made completely out of carbon fiber. Hoyt is the only company on the market that manufactures a bow made out of those materials. With carbon fiber you get a bow that is nearly indestructible, lightweight and isn't cold when handled during winter temperatures. However, you also pay a shiny penny for it, but get a higher level of craftsmanship.