They are used in production all over the place, along with their smaller cousin, the CPLD. If you see a part on a PCB by Xilinx, Altera, Lattice, or some MicroSemi parts, odds are that it's an FPGA. Many FPGAs lose their configuration on power-off, so you configure the bitstream using a CPU for example. As others have said, there are also flash-based ones.

I personally know of many embedded systems using FPGAs (spacecraft and medical applications), signal processing such as radar, many PCIe cards, etc.