The movements in our CrossFit class put significant demands on our hands. Even while wearing gloves many people develop calluses that lead to rips or tears in the skin. Rips and tears are not a sign of good CrossFitting but rather a sign of poor hand maintenance.
Newcomers to CrossFit often begin with callus-free hands. Beginners should gradually build up calluses (by doing CrossFit) to the point where the skin on their hands is tough and thick but also smooth. According to the CrossFit journal “Ideally, your entire palm surface should be one thick callus with no bumps or ridges in any one particular area…. The goal is to maintain an even and consistent thickness of hard skin throughout the entire palm.”
In order to maintain this a CrossFitter should do some basic maintenance on their hands to prevent injury. To start you need to get a pumice stone. During my daily shower I file down my hand calluses so that they are smooth. You can also soak your hands in warm water for about 10 minutes and then use the pumice stone to file them down a bit. Done daily it will keep your hands from looking and feeling terrible and also prevent injury to them.
During the WOD you can use chalk to help keep your hands dry during pull-ups. When lifting be careful not to over-grip the bar. Put the bar where it is going to be not where you necessarily would like it. While under load this is often you fingers and upper palm.
Some people wear lifting gloves and Reebok even has a CrossFit glove that many people in the games used. Remember though that during the games the competitors were doing many WODs over the course of a few days. No matter what their hand conditioning was getting through that many workouts would destroy their hands.
I do not like to use gloves because I want to have tough hands (but not rough hands, there is a difference). It seems to me that there will eventually be a time when I might need to push, pull, or otherwise move something sans gloves and I would like my hands to be conditioned to the task. If you choose to wear gloves it is still important to perform basic hand care.
Many CrossFitters use athletic tape around the fingers and palm where the bar rubs. I will use tape once I have injured my hand but typically do not use it in the normal course of training. Again this is personal preference.