[cmrdporcupine]

If memory bandwidth / transfer speeds between CPU and FPGA wasn't a concern, I can see using an FPGA to "accelerate" some aspects of HTTP protocol parsing -- string tokenizing for headers and the like, being of some small minor value. Or as others have said, further down the protocol layers, handling aspects of TCP/IP and network frames the like.

But that "if" is the problem -- you'll spend more time and CPU shuttling data back and forth than you would gain by specializing the problem in an FPGA.