I recently had my new multi-function-fax-scan-copy-print-coffeemaker go bad on me. It was under warranty, and so I called the folks at Canon USA (according to the IVR they’re in Virginia). The Tech Support Rep (TSR) did a great job and quickly said they’d have a new one on its way. When it didn’t arrive, I called Canon back and they tracked it, showing that what "brown" had done for me was to lose my printer somewhere in Illinois.
The TSR placed me on hold and returned to explain that a supervisor would be calling me within the hour with a solution. The rep then apologized, and apologized again, and then apologized a third time. As he was launching into his fourth round of apologies I finally cut in and said, "Great, I’ll just wait to hear from your supervisor." The supervisor called a few minutes later to explain they were overnighting me a replacement.
While I applaud the TSR at Canon for being empathetic (it’s hard to get most CSRs to apologize once), he provided me with a classic example. Customers want their issue resolved and they want to know you care that they’ve been inconvenienced. Apologizing isn’t like making deposits in your 401k. You don’t get increasing dividends the more deposits you make. In fact, the opposite can generally be true. The more you apologize, the more likely a customer will say, "I don’t want your apology!"
One sincere, timely apology followed by a commitment to resolution will generally suffice nicely.