Most filters ("colour") ones are pretty much redundant with digital photography.
That leaves you with :
Circular Polarisers
Neutral Density
UV
Neutral Density Graduated
Infra Red
and that's about it. There are filters that you only really need in very specific environments, such as hot filters, but you're not likely to come across those.
Very brief explanations :
Circular Polarisers - saturates colours, reduces reflections. Works best 90 degrees to the sun
Neutral Density - Makes you lose a specific amount of light. Good for forcing long exposures.
UV - can be used to cut UV light, handy in bright sunlight - but most use them as lens protection. That is a very debatable subject, though.
ND graduated - as ND but "fades" to clear. Good for exposing properly for both the sky and foreground
Infra Red - cuts out nearly all, or all visible light. Meaning all that's left for your digicams sensor is Infra Red - gives interesting effects.
