You don't NEED any degree to become a professional photographer but studying art and history will be valuable tools both as a photographer and as an informed citizen. The world changes quickly and what may not seen necessary today may become necessary at some point in the future. So... get a degree in SOMETHING with heavy emphasis on art and history.
Meanwhile, shoot everything you see. Digital is cheap; unwanted or duplicate shots can be deleted in seconds -- no harm, no foul. Experiment. Try different angles, exposures, compositions, off-beat subjects -- everything. Use your imagination and perfect your skills. Join a camera club, see every photo exhibit, ask questions, immerse yourself in images.
Learn (or teach yourself) composition, light, shadow and color. They're all important. And you'll find that when you do you'll see things you never saw before; they were always there but most people never see them. Photographers do.
Lastly, there are different kinds of photographers: landscape, architectural, lifestyle, news, fashion, macro and art. Try everything. Find what you like.
Most of the responses I see, here, are good. There isn't a need for a degree, unless there is...
The thing is, you have to be careful about which institutions you choose. Brooks was a mainstay for decades, then, when the market got too tough, they really screwed over their students. The Art Institutes were basically hit and miss depending on faculty (Art Institute of Seattle was known as the "don't hire them, they aren't taught industry best practices, vocabulary, etc., but Chicago's was known for being quite good and competitive).
A Communications minor or focus is one of the most useful things a photographer can learn, especially if being social and approachable/likable isn't already something you are good at. Many of my favorite photographers are actually scientists who either also do photography or whose photography was so phenomenal that everyone stood up and noticed. Those photographs you see from the Space Station, for example, are largely result of experimentation and astronauts getting used to the camera. The one exception is Don Pettit who built the first night-side of earth barndoor tracker on space station by hacking a Russian drill - his photos are taken with scientific precision more often than not.
I would highly recommend at least a two year degree from an art or photography school. While technically in many situations you do not need a degree to work as a professional photographer, especially if going into business for yourself, it is not something that is easily self taught. If you choose not to get a formal education at least try assisting for a working professional to learn the craft. With the many lighting and digital applications today photography can be very involved especially if you want to work on a professional level. A structured education is best to master all of these. A two year degree at a quality photography school should give you a solid understanding of most things and at least some basic business principles are a must. However many employers will require a four year degree which includes a lot of general education such as math, English etc. If you are at some point interested in teaching that and even a master's degree are required. Depending on the route you take many employers will only consider those with some type of degree though I know successful photographers with no formal education.
Although many people interested in photography pursue degrees such as graphic design or fine arts no college degree in generally required. The exception of course would be if you are planning to work for a very specific company that would require a specific degree. There are nationally know photographers who have never set foot inside a university while others may have masters degrees in design. If you are pursuing a degree in one of the arts, I would also recommend a minor in business or at least taking business and marketing classes. These classes will definitely help. Photography is one field where careful planning is an absolute must.
Bob and Chuck have answered this question well. I would only add that a well rounded education in liberal arts would also be a plus especially for a career in photojournalism or editorial photography. Much of photography can be self-taught supplemented by classes in an art school and/or photo workshops. And always be aware that this is a business and the business aspect of it can not be neglected. You need to be a self-starter and be able to make things happen or you'll never get where you want to go.
There are numerous schools offering degrees in photography, but it's not like medicine or the law. Since there are no state exams required, no academic degree is necessary for being a professional photographer.