You can use C or C++ to program FPGAs but it requires some very expensive Highlevel Synthesis software. CatapultC is a product from Mentor Graphics which allows you to write your algorithm in untimed C++. It then synthesizes that C++ into RTL VHDL or Verilog. But CatapultC sells for well over $100,000 so it's definitely not for hobbyists. There's another product called ImpulseC which allows you to write C code which then gets synthesized into RTL, but I'm pretty sure that it only handles C not C++. ImpulseC is about $2000.
For hobbyists, you're probably best off sticking with VHDL or Verilog to describe your design and then using the free tools from Xilinx or Altera to synthesize that code and program the FPGA.