A few years ago, my clients started asking for dyed-mulch, specifically, black-dyed. Being that this mulch is pure wood (no bark), it takes years to decay. An inch or two added every year is now building up to 5 or 6 inches. It is time to remove the thick layer. IMO, anything over 3" depth is too much.
Usually put a thin layer of mulch down over the old, it's only getting put down to incorporate the pre-emergent as well as add color. However, after a few years, you will have built up enough to where you should consider removing old.
If it's getting piled up on tree trunks, remove it. If it's within a couple of inches of house siding, remove it. If its ON house siding, you better remove it PRONTO and hope no critters have decided to use the mulch as a superhighway into the house!