While it is with some caution that I insert myself between Dave and Shawn *grin* I do much prefer cutting on wood. With all due respect to Dave's citation of government regulation I have found that often that regulation isn't based on scientific data.
A couple of other interesting resources:
Cutting Boards - Equipment & Gear - Cooking For Engineers
Michael's Kitchen: Cutting Boards
While I do run boat cooking tools through a dishwasher in general I work with hand cleaning. A couple of my larger pots don't fit in the sink and my cutting boards (one wood for meat, two for veg & cheese (one wood, one small plastic sometimes used for service) , one wood for bread) certainly don't. My practice--right, wrong, or indifferent--is to use a soapy sponge to wipe down the board and then spray with vinegar water (I have sprayers with vinegar and with bleach under the galley sink).
So far nobody died. *grin*
Seriously, no visible sign of growth on the boards. When I had my water system tested for bacteria we swiped the meat and large veg board -- no meaningful bacteria count.