AMD does for their Athlon FX processors, but support is mostly dependent on the motherboard. With that said, most of the AMD motherboards for AM3+ support it, and it's limited to unbuffered ECC.
Unfortunately, that means choosing ECC over power and performance vs. Intel. It's really a sad state of affairs.
They do. Motherboard vendors often fail to support it, unfortunately, but the CPUs generally aren't the weak link.