Asking the question "Which lens should I buy?" is almost the same as asking "What's the best camera to get?", only worse. While there are a wide variety of digital cameras on the market these days, there are literally hundreds of different lenses to choose from and most of them are specifically designed for a certain type of shoot.
Of course, purchasing a lens for each scenario might be a photographer's dream, but the cost - not to mention the weight of lugging all that gear around - makes this impossible for most people. Choosing the right lens depends of several factors, including what you'll be shooting, your budget, what's compatible with your camera body, and what specific features you need.
If you're just starting out and aren't in a position to fork out a lot of money, a "standard zoom" lens such as the Canon 24-105mm or Nikon 18-105mm are high quality, flexible all-rounders. They're great for a wide range of subjects including portraiture, product shots, and street photography, but can also produce excellent macro shots, and landscapes. Sigma and Tamron also make very decent third-party alternatives that are usually cheaper and are used by professionals as well as enthusiasts.
Most serious enthusiasts should have at least a small collection of lenses that cover most - if not all - the scenarios they encounter. Typically, this might consist of a standard zoom, 50mm prime, wide-angle and a telephoto zoom that goes to 200mm or better.
So why would a photographer choose fixed focal length lenses when they already have a zoom that covers that range?
There are several reasons. The first and most important consideration is quality. A fixed focal length lens has fewer moving parts and as the glass inside is specifically designed for one purpose; these prime lenses can provide spectacular results for a very reasonable price.
Secondly, speed. The convenience of a zoom lens and all that additional glass means it is far less efficient with light. Where it would be reasonable to expect an 85mm prime lens to be f1.5, a 70-200mm lens is more likely to have a minimum of f4 or more - unless you really have deep pockets. For example, Canon makes a 70-200mm f4.0 but the same lens at f2.8 is about double the price.
Another important feature to consider when buying a lens is image stabilisation (IS). If you're planning on using the lens for shooting video, the ability for IS to reduce shaking can make or break your shot.
Whatever lens you decide to purchase, remember to look after it. Clean the lens only with a specially made cleaning cloth - never with a tissue or the corner of your shirt. If you treat your lens with respect, it will serve you well and should even outlast your camera body.