Mosaics can be applied to almost anything that doesn't move! (and no this does not mean husbands!) The main characteristic you're looking for is that is solid, although there are many adhesive that will work with flexible materials in the end the surface will not be able to support the weight of tesserae and the grout. The grout will crack and the tiles will fall off.
Surfaces must be solid, free of loose paint, wallpaper, dirt and grease, etc., and must be able to support the weight of the tile and grout. It may be necessary to 'key' the surface by scoring or sanding it so the your adhesive will stick to it.
Cement board - This is exactly what is says. It is a cement based product formed in sheets and reinforced with fiberglass mesh. It is most often used to construct shower surrounds and as a substrate for tile floors. Cement board is weather and water proof, permanent, and readily available at your local home improvement center. Cement board is heavy and can not support itself, it must be screwed in place. Thinset should be used as the adhesive when working with cement board.
Hardibacker - A brand name backerboard that is easier to cut and lighter weight than cement boards. A composite material of cement and cellulose, it is water and mold resistant and secures well with thinset. Hardibacker can not support itself and must be screwed in place to a firm backing. For more information on Hardibacker go to James Hardie's website, (manufacturer of Hardibacker).
Wood - Although wood is readily available one must proceed with caution when selecting this as a base material. Wood is vulnerable to changes in humidity or temperature and can warp or crack, thus popping tiles and cracking grout. if you are going to tile a wood piece such as a dresser or table. Make sure that it properly sealed, free of loose or peeling paint, and sanded to aid in bonding. Do not use sealer's like Thompson's water seal, as they leave a waxy finish that prevents adhesives from sticking. Wood elements from craft stores (frames, shelves, birdhouses, boxes, etc.) are ready for mosaics but are NOT suitable for outdoor use. Wood can be sealed with a 50-50 mixture of WeldBond and water.
Treated and exterior grade lumber also is not a choice. The treatment that it receives is to prevent rot and does not prevent warping.
* Best advice - If you are using wood. Keep it indoors where the humidity is more stable and your piece will not get wet. SEAL IT! Use a high quality bonding primer such as Kilz.
Plywood - Although wood is readily available one must proceed with caution when selecting this as a base material. Wood is vulnerable to changes in humidity or temperature and can warp or crack, thus popping tiles and cracking. It may be used successfully indoors in smaller sizes particularly if it is framed or securely fastened to another stable material.
Glass - Glass makes a great stable surface to work on and if you are using translucent materials you can create beautiful Sun Catchers, etc. Stained Glass makes wonderful tesserae. You can create the look of stained glass windows without the lead, solder, and the fumes. Old windows, table tops, votives, all make great bases for mosaics.
Weldbond and Clear silicones such as Lexel or Dap Clear Silicone work great when adhere glass on glass . One thing to keep in mind when using WeldBond. It goes on white and dries to clear. it can sometimes take weeks if you tesserae is large. (over 1") To speed drying put in a sunny location or over a heat vent. When using large tesserae silicone based adhesives may be a better choice.