Maybe not. This is the time of year when we see people mulching trees incorrectly.  It's called "volcano mulching" and it's bad, bad, bad.  It's a combination of people having maintenance contracts that include seasonal mulching, and ignorance on the part of the property owner and the landscape crew. It's called volcano mulching because the mulch is applied in a sort of cone around the base of  the tree, extending up the trunk. It looks like the trunk is emerging from a little volcano. Sort of. Existing trees don't really need mulch, but there are three good reasons to mulch an existing tree:

• Esthetics: it serves as sort of a frame around the base of the tree; it's tidy
• Weed control: weeds are difficult to remove around the base of a tree unless you hand weed; this is impractical in a large landscape
• Protection: if there aren't any weeds/grass near the trunk, you won't whack it with the lawnmower, string weeder, and so on.  This was, I believe, the original reason that commercial landscapers began mulching around trees. Especially on trees with thin bark (e.g., Japanese maples' beech) you can cause a lot of damage just by banging into it.  This is sometimes called "lawnmower blight" in a rare flash of humor from plant pathologists.

If you do want to mulch established trees, this is how should it be done:

First: keep the mulch away from touching the trunk by 4 to 6 inches.  Mulch that actually touches the trunk encourages damage by voles (mouse-like rodents) that may chew on the bark under cover of the mulch, and encourages fungal diseases because the bark of the tree is continually wet from the mulch.  

Second: keep it level and shallow, three inches deep is plenty.  

This will provide a protective barrier from lawn mowers, accent the base of the tree, and eliminate the risk of doing harm to your tree.