Amun-Min is the god of fertility, and has only one arm and one leg. This is because while the other gods were off fighting, they left him in charge of the tombs and the temples -- he made every woman left behind pregnant. They cut off his arm to punish him.
They went to war again and he remained behind to repeat his offense. This time they cut off his leg. They didn't cut off his penis (perhaps the obvious choice to stop his philandering!) because, well, he was the god of fertility!
Four colors are used when depicting Amun -- Blue,
Green, Black, and White. Black signifies fertility.
When Amun is shown with an erect phallus, he represents Amun-Min.
One of our guides was always embarrassed when talking
about Amun-Min and would refer to the god's most obvious
feature as "if-you-don't-mind-[whispered] erect" or "begging-your-pardon-erect", blushing furiously. It amused me enough that I started asking about Amun-min every time we saw the inscriptions, just to see if he'd blush.
In most places, vandals (often the Copts who lived in he temples) have chipped away the erect phallus because it was deemed inappropriate. At least one of our guides explained that it may have been done by early Egyptians as an attempt to disrupt the power of the god -- how could he be the god of fertility if he was missing the important bits?