I like to work with 1/8th inch plywood in my laser cutter because it's cheap, engraves nicely, and isn't too difficult to cut. One drawback however is it's tendency to warp. Warped plywood will cause the laser to become out of focus when the distance from the lens to the wood changes. This can affect the engrave and cut quality, so one trick I've come up with is to place a strong magnet in each corner of the work piece to hold down any warping. Careful not to let the magnets pinch your fingers though!
Below is a quick video of my laser cutting a 1/4" Poplar coaster.