1. For hotels, where the hotel itself doesn't actually have an online-booking system. Not very common in the U.S., but common among smaller hotels in Europe. Often a third party (most often booking.com) is the only way to book these hotels online.
2. For flights, where Orbitz or Expedia are able to put together a multi-airline itinerary that I can't get those airlines' own sites to return. The last time I used Orbitz was for this reason: it was able to come up with a round-trip ATL-CPH with Delta one way and KLM the other way, with a good price and times that were convenient for me. The fare rules work because they're partner airlines (so it ends up billed as a round-trip, not two one-ways), but I couldn't manage to get either the KLM or Delta websites to offer me that combination, despite quite a bit of fiddling.
I know for a fact Hotel Tonight does this, as I've seen the fax from the front desk clerk with their corporate mastercard number (partly redacted) on it.
Same for flight bookings. I've never found the attraction of booking through third parties; it only adds a failure point. Maybe small or specialized agencies are the exception, like Amex's travel service (which, I think, used a platform like Expedia's, but they had fantastic phone options and would always go figure stuff out on my behalf.)