FIlters:

Don’t waste money on UV Filters
In general I am not a fan of UV filters, they offer little protection from a fall and the glass at the end of your lens is pretty tough, it’s not going to get scratched unless you are very careless. I prefer lens hoods as they do offer some protection from falls and nicely protect the end of the lens from coming into contact with random objects without degrading image quality. I do prefer camera brand lens hoods, I have tried a few of the third party and they often fit just a bit awkwardly making the putting on and taking off just a bit slower. Some of the very cheap 3rd party lens hoods actually use the filter threads to attach, this is bad as it blocks you from adding a filter and is very cumbersome to put on take off.

Circular Polarizer Filters are useful

The one filter I do recommend landscape photographers own (or anyone taking scenic view photos) is a circular polarizer (CP Filter). Some benefits of a CP filter include:

CP filters reduce reflections and glare
Reduces Haze and blue cast in landscapes
Adds saturation to your sky and greenery

More about CP filters. There are other specialized filters worth owning for some situations but a CP is one that many don’t know they need and gives you a look that is not reproducible with post processing. The brands I list I find to be safe choices at each of those price points, there are certainly other brands/choices at each price point.

Budget (Tiffen)
Middle (Hoya)
High-end (B+W)

With all filters, be sure to get the right size screw on for your lens. Ex 77mm. 72mm etc.

Specialty Filters and Systems

ND Filters: ND (Neutral Density) filters are used to take away light in the middle of the day to create longer exposures. As an example, if you want a waterfall to have that silky smooth look, but it is the middle of the day, it will be difficult to take a long exposure as too much light is coming in over exposing the image.
By placing a ND filter on, you reduce light and therefore can do the longer exposure. You can do this for other images as well such as clouds moving and smoothing out a lake.

   

ND Filters Cont: We recommend AVOIDING a Variable ND filter. No matter what the store says to get! The reason is that at higher aperture settings, you can see where the variance changes in your image. It tends to look like a weird X through the image.
ND Filters come in all types of numbers that represent how much light is taken away. from very little (1 stop) to totally dark (10 stop). This is why sales people like to recommend the variable all in one. The darker the filter, the more light you can take away thus creating even longer exposures. 

However, rather than that, using just one or two will usually get the results you like. If you have to choose one for now, start with a 6 Stop ND filter. This will take away 6 stops of light and get you results for most situations you may want.

Again, these are great brands.
Budget (Tiffen)
Middle (Hoya)
High-end (B+W)

Filter Systems: For those that are ready to take their images with filters to the next level and have worked with filters in the past, filter systems such as the Nisi, Breakthrough and Lee are all excellent and high-end systems for the serious photographer. They are expensive but the best.
A filter system simply mounts to the front of your lens, and then you can slide various filters into place for various needs and reasons.