I personally tend to use a stone cutting board. Not sure the exact material, but I'd be inclined to say it's granite. According to this, they do tend to dull knives considerably faster than plastic/wood cutting boards though.
One point the above article mentions is this,
One advantage of stone boards is that they never become grooved or damaged by the knives, and there is an argument that this makes them more hygienic and less likely to harbour bacteria. This is a rather weak argument, however, because if wooden or plastic boards are cleaned and disinfected with bleach regularly they will not harbour bacteria either.
However I think they are undermining this advantage quite a bit. Stone cutting boards can easily be tossed in the dishwasher to be cleaned, unlike plastic or wood cutting boards which may warp. As an average home cook who doesn't like to spend a ton of time cooking and cleaning, this seems considerably more useful to me. I would rather be able to wash my cutting board alongside all my other dishes, than painstakingly disinfect a wood cutting board with bleach regularly.
Dullness of the knives definitely is a real concern, but for my personal preference, I think sharpening my knives every so often is less of a hassle than vigorously scrubbing my cutting board after every use.
To sum up my thoughts,
I'd say avoid plastic. Besides cost, it seems to have all the worst qualities going for it. It can form deep grooves like wood and it can dull your knives if it's a hard plastic.
Wood would be the "ideal choice" for the serious home chef who will take good care of their cutting board. If you're willing to wash it thoroughly, oil it, sand it down once it has deep grooves, etc. then I think that's the best option. It's a bit more dedicated but worth the effort.
Stone if you're lazy about cleaning and don't want to use plastic cutting boards. As I, and others, have mentioned, dulling your blades is a big issue with this type. But for casual home cook use, a duller blade will basically never really struggle with simple tasks like cutting cucumber slices for example.