Although our expertise is in laser cutting plastic (acrylic/Plexiglas, ABS, styrene, and Delrin), we also do cut wood. You can see an example of laser-cut 1/4" red oak at https://www.pololu.com/docs/0J24?section=6.b.
Some things to consider when laser cutting wood:
The laser will char the edges of wood (the degree of charring depends on the resins in the wood and other chemicals, dyes, glues, etc. applied to it).
There will probably be burn marks on the front and back of the wood (the ones on the back might be more prominent since the laser can bounce off of the metal cutting grill and hit the back of the material).
Wood sometimes has denser areas and knots that cause the laser not to cut through all the way; if this happens to your part, we might have to cut twice on those areas, which could degrade the overall quality of the part. This is usually not an issue for sheets less than 1/4" thick and for light woods such as balsa.
The kerf depends on the wood, but it is normally a little more than the kerf on plastic, which is usually around 0.005" - 0.01".
We do not stock wood so you would have to send us some (or have a supplier send some directly to us). The wood must be VERY FLAT (no bowing or warping--otherwise the laser cannot focus), be no larger than 24" x 36" (unless you make special arrangements with us), and it is a very good idea to send extra sheets of wood just in case.
We do not have a particular wood supplier to recommend; other customers have used http://www.midwestproducts.com/, http://www.utrechtart.com/, and http://www.balsausa.com/, which have sent us wood acceptable for laser cutting.
If you are planning to make a large order but are concerned about how your wood parts will look, you might consider getting a small test piece, first. Normally the turn time is just a few days, and test cutting woods starts at around $30-$40 depending on the thickness.
I hope this helps!