Photography is about capturing light though lenses, but choosing the right lens for the job isn't always cut and dry. Lenses for landscape photographers can be particularly difficult to choose because the vast array of options available.
First and foremost, there is no one-size fits all, do everything lens. New photographers often look for the one lens that will do everything and then some, this doesn't exist. There are options to fit your specific needs though, and that's what we're going to explore. The real answer is 12mm-500mm, it really depends on what you're shooting and where you are in relation to it.
Size and weight are also a factor for some photographers. Because most landscape photographers are also hikers, campers and travelers, carrying around twenty or thirty pounds of gear can be daunting, so choosing faster prime lenses instead of a larger, heavier zoom lens means you won't have as much flexibility as a zoom lens provides but the trade off is a significantly lighter load to carry with you.
Fast lenses, or those with a maximum aperture of f/2.8 or faster aren't always needed either, because the sweet spot of most lenses, or where they are sharpest and perform the best, is often between f/8 and f/11.
The wide angle lens is traditionally the go-to lens for landscape photographers. On full frame digital SLR's this would be anything from about 14mm through 35mm, depending on the manufacture. For cropped sensor digital SLRs, specific wide angle lenses, like the Sigma 12-24mm zoom give the equivalent of an 18-36mm lens, still allowing a very wide shot. The wide angle id desirable because it allows for a larger then life perspective on your landscape, capturing what's immediately in front of you, at your feet all the way through the edge of one's peripheral vision. It's the go-to lens for many landscape photographers.
Medium length lenses, say about anything from 40-150mm are great for capturing landscapes as your naked eye sees them, plus or minus taking a few steps towards or from the subject. These lenses generally perform best when the subject matter is more specific, as in the photo below.
This photograph is pretty much how the naked eye sees it, and it conveys a good story, with progression of where it could go.
Longer lenses, also known as tele-photo lenses we'll group into anything 150mm or longer. Traditionally landscape photographers didn't use these, they were utilized by landscape photographers who also shot wildlife, however some are now carrying them for doing detailed shots from a distance. Generally speaking, the investment to return on these lenses doesn't work out, and due to the size and weight carrying them during hiking trips isn't always easy.
Brand and type of lenses also comes up often, and leads to many a heated debated. For many years shooters paired their cameras with the same brand of lenses, i.e. a Nikon owner would buy only Nikon made Nikkor lenses, Canon, Pentax and others the same way. Times have changes for the better and now third party manufactures like Sigma and Tamron bring world class glass to the table, offering solutions that OE companies don't always do. Likewise, old school photographers really like prime lenses, or fixed focal length lenses because of the sharpness and maximum aperture, often one to three stops faster then a zoom. Zoom lenses became popular because they offered a wide variety of coverage in a package that was easy to handle. Neither is better, both have a time and place and your particular style will dictate which lens you use for each shot. For some shooters, walking an extra twenty feet closer because they have a prime lens isn't a big deal, whereas walking twenty feet closer to your subject may not always be an option if you are already on the bank of a river or edge of a lake.
Lastly is a look at lens accessories. Because some of the most stunning landscapes are shot during sunrise and sunset, this often puts the sun in a direct line of sight with the lens, causing nasty lens flare. Ovoid this by utilizing a proper lens hood to reduce the amount of flare. In some cases you may even find holding your hand above the lens, beyond the hood can help block more lens flare; a hat, magazine or any other large object can also be used. The other advantage of a lens hood is it helps protect the lens element against accidental bumps and because of the shadowing from stray sunlight, photos tend to be deeper and richer in color. Additionally, a quality UV filter should almost always be used on the lens to help protect against moisture, sun flair and glare and accidental touches. Creative filters, like the Cokin system can add dramatic effects, like this photo below with the burnt tobacco colored sky, a result of a graduated filter.