Having the right gear is a critical foundation for landscape photography. It’s possible to get lost down a (very expensive) rabbit hole looking for the ‘perfect’ gear, so I usually recommend simply going for the ‘good enough’ gear. Honestly, so much comes down to the way in which you use the gear you have, so most people would generally be better off focusing on developing skills and techniques rather than worrying too much about having the right gear.
That said, lenses are some of the most important gear in your kit, as few other items will have as much of an impact on the types of images you can shoot and on overall image quality. In this short 10 minute video, Nigel Danson goes over three main lenses he uses for his landscape photography kit: a wide angle, a fast prime, and a longer zoom lens.
Watch the Video

I shot this PNW forest scene with a wide angle lens (11mm on a crop sensor). The wide angle allowed me to capture the cascading water and surrounding trees all in one image, but it also makes everything look smaller and more distant.
Wide Angle Lens (Your Workhorse)
The first lens that Nigel discusses is a wide angle lens. He uses a Nikon Nikkor 16-35mm f/4 lens, which he likes for its ability to easily fit various lens filters on it. That’s a solid lens, and there are certainly quite a few others out there worth considering. Pay particular attention to compatibility with your camera body, focal lengths covered, sharpness (check out dxomark.com for testing results on a huge database of lenses), filter size, and aperture. You might also consider weight if you plan on doing much hiking or traveling with it. I personally use a Tokina 11-16mm f/2.8 Pro DX-II lens, which I love for its sharpness, wide field of view, and wide open aperture. It is unfortunately rather heavy.
The wide angle lens is my workhorse lens, as it is for many landscape photographers. The wide angle lens is great for providing a more unique image, for being able to include more elements from the scene into a single shot, and as Nigel points out, for offering outstanding depth of field. When you set the aperture to say around f/8 or f/10, the hyperfocal rule means that nearly everything in your image both near and far will be in focus.
50mm Prime Lens (“Nifty Fifty”)
The second lens highlighted is a “nifty-fifty.” A nifty fifty is a 50mm prime lens (a prime lens is a lens that has a fixed focal length, meaning you can’t zoom in or out). He talks about how a prime lens usually offers superior optical quality (since there are fewer moving pieces; a zoom lens tries to allow for good optics at different focal lengths, while a prime lens lets the lens maker focus on getting the optics just right for that one particular focal length), and also notes that there are other prime focal lengths on the market, such as a 35mm prime. Many of these also can have very fast (aka very wide) apertures, sometimes as much as f/1.4! This allows for great bokeh (blurry backgrounds behind an in-focus subject) and gives you more flexibility in low light situations.

This scene was shot using a long zoom lens in Kenai Fjords National Park. I was several hundred yards away on a boat, but the zoom allowed me to get in close on the bird flying over a giant piece of ice that had recently calved
Telephoto Zoom Lens (70–200mm)
The final lens he talks about is a longer zoom lens (he uses a 70-200mm f/2.8 Nikon lens). A long lens like this allows you to really zero in on your subject, for instance when lighting conditions are lackluster. With a zoom lens, you can compress the image quite a bit, making distant objects seem larger and closer. He also describes how you could even get quite creative with using a zoom lens for macro shooting and making your subject and background intentionally out of focus.
In all, a great, short video with some helpful examples and explanation about three different types of lenses all landscape photographers should have in their kits.