For example, if 802.11b devices had been built using FPGAs, an upgrade to 802.11g could have been an OTA update. Or a new Bluetooth variant emerges (e.g. BLE) and support could be added to computers and phones overnight.
For these applications it's useful to think of an FPGA as a chip that you can patch, upgrade or reconfigure for new applications. However, looking at it from another angle, we can think of it as software that isn't limited by the CPU architecture.
This second category opens up the possibility of crypto algorithms that don't suffer from the timing attacks that they do on the CPU. Or a video codec that can be designed without having to worry about which extensions the CPU supports.
I'm sure there are much better examples and some of these are bad ideas that would work better on a CPU, but hopefully that gives you some ideas.