As moore's law no longer holds true for CPU, there is increasing interest turning to FPGAs. You can create a truly bespoke Processor for any task.
Of course this is trade of between development time / cost vs processing needs of task.
I suspect FPGAs demand to only increse over the coming years. Intel's integration of FPGA into their line of processors is a promising step and sign of where things may be heading.
Will we see a new generation of JITs emitting FPGA code?
JIT for FPGA is quite possibly mathematically impossible.
It's much better if you regard an FPGA as a set of pluggable fixed-function dataflow integer pipelines than a processor. Something that you stream data into and get a transformed version out. It's much less recognisable than even a GPU.
Consider it the next step beyond SSE/MMX for configurable arithmetic kernels. The one thing on-die FPGAs will definitely help with is cryptography.
At the moment, most of those task would be done on ASIC, so yes we might see those tasks done on FPGA.
There wouldn't be advantage in performance generally, only in that you could have true HW updates.
It is something I've been thinking about in that you could theoretically have a processor optimized for the game. So you could download HW on the fly (pre built) and flash your machines FPGA.
why ?