They are essentially low-volume ASIC replacements. Some applications:

- digital signal processing (DSP)

- network equipment (modern high-end FPGAs are able to function as 100G Ethernet switches and routers, just connect them to some PHYs and fast DRAM)

- systems on chip (SoC): processor, fast DSP, all kinds of IOs, memory controller – all on a single chip

- realtime video stream processing

For more examples, see http://www.xilinx.com/applications/index.htm