Clear or UV Filter - Protects front element of lens, very very nice thing to have, some people say lens hood enough, I'm kiasu and kiasi, so I put a clear filter on as well.
Circular Polarizer Filter (CPL) - offers same front element protection, looks like 2 uv filters screwed onto one another, you can rotate the "outside" one when mounted on your lens to either give you deeper blues from the skies or to cut through reflections in glass
Neutral Density (ND) filters - Have limited experience with these, they stop some light front entering the lens, offering the photographer more flexibility in terms of shutter speed and aperture, (say they want a long exposure, but its a tad bit bright for the shutter speed, so put on the ND filter to drop light entering, without needing to up f/stop)
Graduated Neutral Density (GND) - half of the filter is of neutral density which transitions, either abruptly or gradually, into the other half which is clear. Used to bring an overly-bright part of a scene into the dynamic range of the sensor, think of it as Half-ND, Half-Clear.
And what are the basic filters that most photographer should have?
- Clear/UV filter , because you don't want to end up with chips or scratches on your front element
- CPL, very useful for getting more dramatic deep blue skies, and you can cut through reflections in glass or water (how much is dependant on the quality of the filter)
Any difference between brands of filters? Is it very expensive?
- B+W The most expensive, but also the best, easy to clean, good quality etc etc, 1 clear filter for 77mm thread is $130 or $160?
But as Lordpain mentioned, Hoya is good enough for most people.