Now shooting digital almost exclusively, by far my most used filters are CPL. There are numerous different uses for CPL and a lot of what they do is difficult or impossible to replicate in digital post-processing (unlike most other filters).
ND filters are useful for longer shutter speeds, which can be used to give motion blur to moving water (as illustrated quite well in several other responses).
That's not the only use for solid ND filters, though. Longer shutter speeds also can be useful to make traffic or even pedestrians "disappear" from city scenes and roadways. A moving vehicle or walking person will not be recorded in a long exposure made possible with a fairly strong ND filter. Other possible long exposure uses: fireworks, aurora borealis. Another common use for solid ND filters is to allow larger apertures in relatively bright conditions, as might be wanted for shallow depth of field effects. A very strong ND is necessary when viewing or shooting a solar eclipse.
Photographers shooting stills probably only need one or two or at most three ND filters for specific lenses that they use for some of the above purposes... Probably the single most useful would be a 6-stop. A good pairing maybe a 3-stop and 6-stop, which can be stacked for 9 stops. Some might prefer a 10-stop (especially with wide lenses where you can't stack filters). Filters used for solar eclipses are even stronger... some 15 or 16 stops!
Videographers, on the other hand, may need a wider variety of ND filters in order to fine tune exposure. That's because they have less exposure latitude to work with. The apertures are the same, but they have less adjustability with shutter speed and ISO may be limited as well.
For both photographers and videographers, the best quality is with fixed strength ND filters. But because they need a wider variety, videographers in particular might instead choose to use a Variable ND filter. However, those often compromise image quality. Plus even the lower quality ones tend to be rather expensive, while better ones tend to be extremely expensive.
I've stopped using Graduated ND filters. They're bulky to haul around, fussy to set up and use, easily damaged plastic or expensive/heavy/fragile glass, difficult to shade from sun, don't work all that well and simply aren't necessary with digital. With multi-shot or multi-processed images, plus layers and masks in post-processing I can do a better job of balancing scenes than was ever possible with Grad ND filters. I've still got a few Grad NDs, but have only kept them in case I shoot some film (in other words, those filters are largely just gathering dust).
I haven't used them a lot recently either, but have a handful of what I call "portrait" filters. Those are "black spot" or "black splatter" and "black mesh" filters that
reduce fine detail to make some types of portraits "kinder" to their subjects. A couple of those are homemade... black mesh materials that I sandwiched between a couple filter rings without any glass in them. The "black spot/spatter" filters were bought that way. The filters with black are color neutral and are the only type I have now. There are also flesh colored and white, but they effect color and I've never been a fan of them. Some wedding photographers like the white spatter or white mesh filters for the somewhat "dreamy" effect they can make. There also are clear spatter, the weaker of which create sort of a glow while the stronger ones make for a more "foggy" looking image. Some of these filter effects can now be pretty easily done digitally in post-processing.
Another type of filter I still carry around but don't use very much are UV, which are primarily just for "protection" on the rare occasions when I find myself shooting in situations that might be risky for my lenses. I deliberately carry UV (instead of "clear" protection) because there are occasionally times a UV filter can be used to reduce bluish haze in scenic shots too. Digital doesn't require the original use of those filters with film, which was overly sensitive to UV light and would show pretty strong tints from it, particularly in images taken at higher altitudes where UV is more prevalent.
I have also kept some of the filters I used with black & white film, just in case I end up shooting some. But I don't use them to make digital B&W images.... only film. When I do B&W digitally I shoot in color, then convert to B&W in post-processing. The filter effects are easily applied to digitally generated B&W images, during the conversion process.
Instead of color correction and color conversion filters I used with film, I now carry a small set of "Warm Cards":
https://www.vortexmediastore.com/pages/warmcards-white-balance-system. Those are used to set a custom white balance with a slight color bias. The set has several cards with different strength cyan tints, which cause a warmer image. They also include a couple with yellow tints used to make images cooler, as well as a greenish card that's used to help balance color better under fluorescent lighting. The last card in the set is pure white on one side and neutral 18% gray on the other, so either side can be used to set a custom white balance without any color bias, while the gray side also can be used to help dial in an accurate exposure. In the past when shooting film I instead used a variety of filters for these purposes. Now with digital the same can be accomplished even more accurately using a custom white balance.