If I want to use slow shutter speeds on a bright day, which filters are appropriate.
Filters modify the light that reaches the sensor. Depending on the type of filter they may allow only certain colors to pass (colored filters), reduce the amount of light reaching the sensor without regard to color (neutral density filters), allow only polarized light (polarizers), diffuse the light slightly (soft focus filters), cause certain kinds of highlights (e.g. starburst filters), etc.
If you want to decrease the shutter speed you're using (longer exposures) without reducing aperture or sensitivity (ISO), you can use a neutral density filter to block some of the light. Think of it as sunglasses for your lens -- it's a gray looking filter that simply absorbs some light. They come in different densities, and you can even get a gradient ND filter that'll block more light from one side of the image than from the other. These last are used, for example, to darken the sky without darkening the foreground.
There are two types of filters that are commonly used to reduce the overall amount of light.
Neutral Density Filters: Reduce the amount of light entering the lens without changing the color of the light. Densities are expressed in terms of stops. An ND2 filter will reduce the amount of light by two stops, which allows 1/4 the total amount of light that would enter the lens without the filter. An ND 8 would reduce the light by 8 stops. Variable ND filters are available that contain two elements that change the overall density as one is rotated in relation to the other. Quality variable ND filters can be quite expensive (A Singh-Ray 77mm Thin Mount Variable ND filter goes for about $400). A graduated ND filter has one edge that is darker than the other and can be useful when the sky is very bright and the foreground of the scene you are photographing is darker.
Polarizer Filters: Alter the type of light entering the lens by only allowing light polarized in one direction to pass through. Without getting too technical, polarizers will decrease the total amount of light reaching the lens, reduce or even eliminate reflections off of water or glass and metallic objects, increase contrast, and increase the saturation of certain colors. They have a marked effect on blue skies and green vegetation and are popular with many landscape photographers for this reason. Most polarizers reduce the amount of light reaching the lens by about 2 stops, but it does vary from one to the next. In order for Auto Focus systems to work a circular polarizer must be used.
It is also possible to combine a polarizer and ND filter for additional reduction of the total light reaching the lens. When stacking filters attention must be made to vignetting, especially on wider angle lenses.
For how to use a polarizer, see How does one use circular polarizers?