I use filters for protecting the lens so when I need them, they get dirty—situations involving sand/dust, salt spray, rain and or other hazards, like children with fingers. Or with my polarizers, I tend to fingerprint them eventually all on my own.
When I do use filters, I like them to be pristine, because they can affect image quality even when spotless; see Filters: Loss of Image Contrast With a Polarizer (Zeiss 35/1.4 Distagon) in Making Sharp Images.
When home, I use a special soap to clean filters under warm water: Optisoap from OptiKem. It’s designed for contact lens wearers and leaves zero residue. Using a tiny dab on a filter with warm water and gentle fingers removes all particulate matter as well as grease and oil, with zero risk of scratching. However, NOT recommended for polarizers, since they are not necessarily sealed (use only with regular glass filters).
You’ve got to love those amphoteric surfactants. Optisoap is hard to find online, but local optometrists often have it.
You can order Optisoap directly from Optikem International in Denver, CO at (800) 525-1752 / (303) 936-1137. It’s $18.50 for a 1 quart bottle, which lasts a long time and is vastly less expensive than the tiny bottles you might buy elsewhere. See also SereineSolutions.com.
Get filters at B&H Photo. At present my preferred filter brand is Zeiss, and I also like Heliopan. I’ve had terrible luck with B+W polarizers—very stiff rotation and binding.