Actually pretty handy for doing optimized NIC/protocol processing. Particularly handy for wireless stuff IIRC. It's about as close as you can get to a software defined CPU, so the options are kind of limitless.
Learning & prototyping hardware (ASIC) design. Applications that like low latency I/O. You can respond in microseconds with real time guarantees, eg for radio link layer protocols.
Just to toss out a few ideas: software defined radio, high-throughput DSP (like audio processing or machine vision), MITMing of fast protocols, packet inspection, CPU emulation.