Yes.
BUT, they have to be taken care of. Every month or two they must be "seasoned", which involves rubbing them down with mineral oil and salt, so that juices from meat or vegetables don't soak in and harbour bacteria.
They are probably the safest if taken care of. Plastic ones are the worst offenders, as they cut rather easily, giving bacteria a place to hide.
(can you tell I love my wooden cutting board?)