I have the same 10W laser as Ryan, and it will cut 3/8" pine, but with either a lot of passes or by going veryyyyy slow.
The slow cut will leave a slight taper on the edge. So much depends on the wood type and color. Now the only thicker material I will try to cut is cheap 1/8" wafer board to make router templates for anything thicker. Bummer is that reduces the ability to get sharp concave features less than the router bit diameter.

I can cut certain colors of 1/4" masonite with a few passes, but depending on the brand, stuff with different resins will not cut at all and some will cut fairly easy. 
Either way, running at near full power will take a % of the diodes working life away. The relationship is not linear, degradation is much faster at higher power, so I usually opt for more passes at lower power (usually max 50-70%) with a lower speed.

The sprays are a great tool for diodes, really expands what they can do.