Morale Patches are an unofficial military tradition that has exploded in the past few years. The trend has been helped along by the increase in Private Military Conctractors who aren't subject to the same rules about uniform wear, and the Army's increased use of velcro on uniforms and equipment. It's real easy now for grunts to peel off an offending patch before someone in the chain of command spots the unapproved item.
Above is a selection of common morale patches. As you can see there is a patch for every mood and sentiment. Some are in good taste, while others are risque.