Why use an FPGA instead of a CPU or GPU?

Recently, Intel bought Altera, one of the largest producers of FPGAs. Intel paid a whopping $16.7 billion, making it their largest acquisition ever. In other news, Microsoft is using FPGAs in its data centers, and Amazon is offering them on their cloud services. Previously, these FPGAs were mainly used in electronics engineering, but not so much in software engineering. Are FPGAs about to take off and become serious alternatives to CPUs and GPUs?

FPGAs are used extensively by e.g. the Amiga community to recreate older chipsets.