for FPGAs the only switching technologies used are: SRAM and antifuse.
Xilinx, Altera and AT&T FPGAs are SRAM-based, while Actel and Quicklogic FPGAs are anti-fuse-based. Xilinx also produces antifuse-based FPGAs.
they don't use the EPROM and EEPROM transistors for FPGAs, these are used with CPLDs.
Xilinx recently introduced the Spartan-3AN. It includes a built-in non-volatile flash PROM that can be used to configure the FPGA after power-up, or to store other user data. That saves some space on your PC board. All Xilinx FPGAs use volatile SRAM to store the active configuration during run-time. I'm not very familiar with other FPGA manufacturers.
with Altera device. program is saved in FLASH memory to configue FPGA after powerup, and also have some configuration device( use MAXII) .For best overview you should log on their website for more information