You're going to get a lot of "favorite" beddings listed on your answers, just so you know. Traditionally, people used straw. About 4 decades or so ago, horseman started buying packages of pine shavings, and that has been very popular. I use these two plus a product that is fairly new, with several different names. I buy the manufacturer's product named, "Equi-Fresh." It's made from pine sawdust which is cooked into a gravy, extruded into pellets and the pellets are dried hard. The packaging tells you to spray them with water. I don't. I put about 2 bags in the spots in the stall that my horses like to urinate, and I put shavings on top of them. It has the ability to soak up the urine, turn to a powder and then, soak it up a 2nd time. Bc it's pine it breaks down really quickly and can be used as garden fertilizer. It's a GREAT deodorizer.
Some folks use rice hulls, and I've heard of shredded paper, but I've never seen it for sale in my area, else I would have bought some to try. Maybe somebody else has used this?!?
FYI-- You cannot use other wood shavings--even if they are free for the taking bc most other woods are toxic to your horse. A horse will soak up the toxicity through their hooves.