A few thoughts:
1) filters are made of very thin glass. As a result they will crack and shatter very easily compared to most front element glass, which is considerably thicker. The problem here is that if you use a filter for protection it will only protect against light debris and liquids. Anything hard or a significant drop will crack the filter and that means shattered glass - highly abrasive shattered glass likely blowing all over your front element.
Note there are lots of claims of people dropping a lens with the filter on and the filter "taking the fall" and cracking and not the front element. Its highly likely that the filter had no part in the protection at all, might have actually caused more harm than good with cracked glass shards/dust and also can very often end up getting its filter threading caught on the cameras - which makes it hard to remove and also can end up messing up your lenses filter thread.
2) A UV filter cuts down on UV light entering the camera, however most digital cameras already take account of UV and have built in blockers. Thus UV filters really only cut down on UV once you're in higher than average conditions - such as above 5000feet.
3) A Polarizer polarizes the light. This has the effect of cutting down on reflections from non-metalic sources. IT can be great for getting shots on water without reflections playing a part in the shot. When used at right angles to the sun it also helps give a nice deep blue cast to a clear sky.
The downside is that it will take away between 1 and 2 stops of light (varies between models). This will, as a result, affect your exposures so you might find if you're shooting action or in dimmer conditions that the 1 stop loss is a hindrance.
In the end there is nothing to stop you stacking filters (although note some brands make ultra thin filters that have no front thread on them - so they would not stack unless placed on last); however I would say that unless you're going to need and benefit from the effect the filter has, then there is no point using it.
If you want one for protection a clear glass filter is all you need. Remember though its only going to stop light objects. Ideal at a sandy beach on a windy day or in wetter conditions - no use for stones or paintballs nor drops to the ground.
Note that in most situations a lens hood provides all the protection you'll need on an average day.