YES, as long as you apply it correctly.
Mulch has many benefits, including preventing disease, supplementing nutrients, and helping a tree conserve water. Mulch also protects soil from extreme temperatures by keeping it cooler in hot conditions and warmer in cold conditions. Finally, mulch helps prevent soil from getting compacted, which starves a tree of oxygen and moisture. Scientists have found that mulched newly-planted trees have a much better survival rate than non-mulched trees, so the extra time and possible cost of laying down mulch are well worth it.
Not all mulch is equal. Coarse woody mulch (as opposed to living mulch, such as turf grass) seems to have the most benefits, and almost no negative consequences. Coarse woody mulch is generally deters invasive plants and disease.
Mulch is often available and delivered for free by local tree services.
How to Lay Down Mulch
Cover the ground under the tree with a layer of mulch 3-4 inches thick. Start at about 1 foot away from the trunk, not right next to it (as you see at right below; this is also called "volcano mulching," which will harm and possibly kill the tree). Put down mulch all the way out to the outside edge of the tree’s canopy (the drip line) if possible. Try to use hardwood chips for hardwoods, and pine chips for pine trees.