It's an unfair question since no one can guess individual needs, considering there are so many variables. What do you have already? What do you like taking pictures of? What is your budget? What is the intended end use of your images? What kind of camera do you have? What is... well, you get the idea.
While the above question may be a common one the core problem is the lack of knowledge about lenses in general. I will try to cover some of the more common answers here, just keep in mind that it is by no means complete nor comprehensive.
What's in a name? Like anything else in our commercially saturated life there are name brands, off-brands and then there are knock offs. Quality lies with the name brands, obviously, but you will be paying top dollar for them. However, even with name brands there are levels of quality. For example, Nikon and Canon, two of the biggest names, each offer consumer level and pro level gear.
Canon and Nikkor are recognizable for quality but there are other top level competitors such as Zeiss, Leica and Pentax. Don't forget players like Tamron and Sigma that offer the consumer considerably decent quality at very reasonable prices. Lens quality from these two can be as good as many of the name brands but with a significant cost savings. Then there are the off-brand names like Bower and Kenko that offer lesser quality but if quality is not a factor and saving money is, then a serious look at some of these lenses may be in order. Lastly there are the novelty lenses such as those offered by Lensbaby and Holga. Often considered gimmicky among many pros, they do have a loyal following with many hobbyists.
Beware though, while your experience and finances can be an influencing factor at the time of purchase they are very temporary factors. Your experience will advance and you can always save for better glass.
Types of Lenses are categorized into two main classifications; prime lenses and zoom lenses. Prime lenses have a fixed focal length with the common standard being the 50mm lens. The industry standard of classification considers anything under 50mm to be a wide angle lens while anything over 50mm goes into the telephoto range. As an example, a 35mm lens would be a wide lens while 100mm would be a telephoto lens.
Zoom lenses have variable focal lengths. A turn of the lens barrel adjusts the focal length from one end of it's focal range to the other. For example; a 24-200mm lens can go from 24mm wide angle to a 200mm telephoto lens just by adjusting the lens.
Focal Length refers to the angle of view and magnification a particular lens can handle. It's actually more technically complicated than that, but for the purpose of this article the easiest way of thinking of focal length is how close your subject will appear in the frame. This is based on the focusing distance of the glass elements to the digital sensor, measured in millimeters.
Macro and Focusing Distances relate to how close to a subject a lens can focus. While all lenses can focus on infinity, the minimum distances can vary from lens to lens. You will need to read the individual lens' specifications to determine minimum focus distances. Some lenses have the ability to focus at more extreme close distances. These are given the designation of being a macro lens. Focusing distances for a macro lens can usually be measured by inches rather than by feet compared to a regular lens.
Speed of a lens is determined by its aperture opening. The bigger the opening the more light can enter the lens, making that particular lens more effective for lower light situations. The larger opening in the lens allows you to gain a stop or two in shutter speed over a standard grade lens, hence the term fast lens.
Vibration Reduction is a mechanical feature on a lens that compensates for unsteady hands. Manufacturers have proclaimed that this feature can gain up to two stops of effective hand holding ability in capturing a scene. While this is hard to prove, this feature can help in minimizing blur from unsteady hands. Just remember that this feature can introduce blur when used with a tripod. Turn off vibration controls when a camera is sitting on a tripod.
Image Projection Size refers to the size of the projected scene onto the camera sensor, or image circle. In short it simply establishes whether a lens is designed for a full frame camera or a crop frame camera.
In basic principles, a lens works by projecting the light entering the barrel onto the sensor plane behind it. The point of focus is based on the focal length of the lens. By default, the projected light is circular. It is the shape of the sensor that gives us that familiar rectangular aspect.
In the same respect, a crop frame lens will project an image circle large enough to cover a crop frame sensor. Obviously that circle will be much smaller than that of a full frame lens. This is important to note as it makes deciding on what kind of lens to buy somewhat critical.
Where the real issue of incompatibility presents itself is with crop frame lenses on a full frame sensor. Aside from the image circle being too small to fill a full frame sensor, there are often mechanical considerations in the building of the lens. Many crop frame lenses have rear elements that protrude further back than a full frame lens that can cause physical damage to a camera's mirror or sensor. If you are unsure, ask a sales representative to help you with lens choices.
Construction Quality is probably the one factor that plays an important role in pricing. For the most part, when it comes to lenses, you get what you pay for. The funny thing is that quality is seldom seen from the outside. It's what is inside that really matters and even then it's seldom about the bells and whistles.
Take a simple single element lens, for example. In this kind of lens the curvature of the glass element bends light to focus at a specific point behind the lens (focal distance). This bending causes chromatic aberrations, or the misalignment of color spectrum, because of the curvature of the glass. In order to correct for this misalignment additional elements are introduced. Now it starts to get complicated. If that's not enough to make an engineer pull hair let's complicate things and make it a zoom lens. Now not only do the elements need to bend light properly it has to do it at various focal distances and that's where the big bucks go.
Hopefully this information gives you an introduction into the various types of lenses and can help you decide your next lens purchase.