There's tons of filters out there but the most important thing is to make sure you skip those dirt cheap filters as they don't do much other than degrade the quality of your images. I used UV filters as accidental drop protection (and I really liked being able to wipe the it clean with my sleeve) but I found they caused too many flares.
UV filters supposedly protect your sensor from harmful ultra-violet rays. A UV filter will have no visible effect on your images.
Polarizing filters work the same way that polarized shades do - they cut down on glare, haze and reflections. They darken skies by cutting through atmospheric haze and they'll allow you to shoot bodies of water and glass buildings as they appear to your eyes.
Neutral density filters reduce the light by a specific number of stops. They're darkly colored and can be stacked on top of each other to allow you to shoot long exposures under brightly lit conditions. These are helpful in any situation in which the sky is dramatically brighter than the lower half of your frame or if you'd like to mute the light a bit to allow some motion in your shot (like a blurred field of wheat from moving in the wind on a bright day.)
There are plenty of filters out there - read up on the different types
here and tailor your purchase to suit the look you're going for.
And if I may be corrected anywhere - forgive me, I'm watching a Pink Floyd concert while typing.
