In the 80s filters to create purple or tobacco skies were very fashionable, together with star effects filters and artificial rainbows.
Nowadays, use of filters is much more restrained and they are primarily used to enhance in a more subtle way what is already present in an image.
To protect your lens a skylight or UV filter can be left on permanently. They cut down haze or blueness at the beach or in the mountains.
The 81-series warm-up and Soft focus filters can be used to create romantic portraits or landscapes. Their effects however can be quite easily created in your digital darkroom which eliminates the need to buy expensive filters.
Polarizers and gray graduates are arguably the most useful.
A polarizing filter eliminates reflections on shiny surfaces, saturates colors and deepens blue skies. The degree of polarization you get depends on the position of the filter in relation to the lens and the lighting. They work best in sunny conditions.
Gray graduates will prevent the sky from washing out in relation to its foreground. To produce a natural looking effect you need to line up the graduated part of the filter with the horizon. Square filter systems such as produced by Lee or Cokin allow you to slide the filter up and down in its mount until it is exactly where you want it. Using a larger aperture such as f 5.6 will make the join less obvious.