Epoxy is possibly the most hard-core bonding material. It's a good choice for gluing wood over a marble fireplace if you want a bond that cannot be broken other than by natural disasters or power tools. Once epoxy sets, it is harder than the marble tile itself. Because it bonds to anything, you can stick any type of wood you want to the surface of the marble using epoxy.
Although they take longer to set up than other options, silicone adhesives are easy to find at local home-improvement stores. Silicone adhesives are designed to work with different materials, so simply read the package to determine if the silicone you want to use is rated for use with wood and marble. Do not attempt to use a silicone caulk that isn’t rated for use with both materials.
Another alternative is polyurethane glue, which is a specially designed mixture that some professionals prefer over silicone. It works in a similar fashion and can be used with many materials. It is hard to work with, especially in colder months when the adhesive stiffens, but the end result is an adhesive that will last for years.
All-purpose adhesives can be found at any local home improvement store along with the other glues for wood and marble. Just as with silicone-based adhesives, you must read the container before you purchase a general-purpose adhesive to ensure it is rated for use with marble and wood.