It's April 15th once again, here in the United States that's Tax Day.
The worst IVR system we ever tested was an IRS system called "TeleTax," which is still in use: 800-829-4477. We did this test as part of the calibration of our process many years ago, so it wasn't a client project (and hence I'm not under NDA about it).
TeleTax lets callers listen to prerecorded informational messages on about 100 topics, and the interface is almost completely unusable. In order to hear a given message, you need to know a three-digit code identifying the particular recording you want. For example, "100" plays a recording listing the kinds of IRS help which are available to taxpayers.
If you don't happen to know the code for the information you want, there is an index available--but just navigating to the index takes over two minutes thanks to all the helpful hints about getting information from the IRS' web site (not a bad strategy, actually). No live help is available on the TeleTax line.
Worse, the system appears to have been generally neglected (again, not surprising, since I doubt many taxpayers actually find this a useful resource) with some bugs and general degradation. When I entered "253" to access a recording about alternative tax forms, I got the message "That is not a valid entry. Please enter your social security number." Apparently at some point, "2" was turned into a universal option for transferring out to the refund status line--probably when someone discovered that the vast majority of callers to TeleTax actually wanted to check on their tax refund and called the wrong number--but the entries were not reindexed to take this change into account.
So no matter how bad the IVR jail at your least-favorite bank or airline, you can take comfort in this: the IRS is worse.