Mmmm... Just to bring up a different perspective, keep in mind that many of the ancient Middle Eastern and even Greek deities were actually local religions. As in, every city or tribe had its own God. Polytheism arose because of the clash of these different cultures - as VoidPointer said, when a city-state lost a war, it was because their god had lost to the other city's god. The people were originally monotheistic in their one local god, but as their villages grew into cities with many other people's faiths, everyone's personal gods got mixed into some giant melting pot of deity soup.
It was actually a major problem that so many different deities overlapped - Athens's Athena was a war goddess, as was Sparta's Ares. (Well, except for the "goddess" part.)
Shinto, the ancient native religion of Japan, practically had gods hiding behind every other rock. Literally every mountain or forest had at least one god. There were 7 gods for rice.
Mountain of Faith, the Touhou game I referred to a page ago, actually had half the cast made of goddesses the player slaps silly, including twin goddesses of Autumn, one for harvest, and the other for the turning color of the leaves... and they're such utter small fry deities that they're considered some of the weakest beings in Gensokyo. (And the player character actually goes around mugging all sorts of fairies and goddesses and monsters of their faith so that she can have it for herself as a powerup! Of course, the whole plot of Mountain of Faith is that it's basically a religious turf war.)
And hey, there's the
Odd Job Gods page on TVTropes, which has this under "Real Life":
- Given the sheer size of their pantheon, it's no wonder that the ancient Egyptians had a lot of these, including:
- Nefertem, the god of perfumes and lotuses.
- Iabet, the goddess of the East.
- Hu, the god of voice of authority.
- Sopedu, the god of borders.
- Seker, the god of the necropolis of Memphis.
- Mafdet, the goddess or snakes and scorpions.
- Tayer, the goddess of weaving.
- Satet, the goddess of inundation.
- Ihy, the god of music and beer.
- Shay, the god of destiny.
- Qadesh, the goddess of ecstasy.
So, anyway, what I'm saying is that "god" can be a fairly expansive term... I'm thinking that gods should actually be based on a system of being associated with one or more spheres, but basically just being a normal version of whatever their base creature is, unless they can draw power from their spheres.
Spheres give power based upon the influence the sphere has in a region, as well as based upon worshipper faith, and possibly gets boosted with some kind of sacrifice or festivals.
Of course, when you have your god literally living in the next house over, "Sacrifice" would mean brining them a barrel of their favorite drink and some masterwork prepared meals. And really, when we talk about dwarven gods, we all know we're talking about someone who isn't just a great "drinking buddy", but someone who could drink you under the table. Heck, a dwarven god should be able to drink demons and other supernatural beings under the table! (I mean, dwarves drink 10.25 gallons of alcohol in a sitting, after all...)
(It's surprisingly hard to find images of God or even Thor getting drunk on Google.)
edit: ah, and spheres should be the key to deific power - gaining access to a sphere is what puts someone on the path to godhood. You can probably steal spheres from defeated gods, or force them to share it. Gods that share spheres split the power that the sphere gives them. As such, while they can try to cooperatively "enlarge the pie", and make the sphere larger and more poweful, they can also try to zero-sum steal the spheres of others, or cut off access to spheres that one is sharing with other deities to increase one's godly might.
As such, godly powers are doled out in limited quantities. Starting from nothing, you can start getting little bits of the powers that Neovonik was talking about, like regenerative powers, and/or upgrading the stuff your flesh is made out of to something harder than adamantine. Your size can potentially increase, if you want, but it may be best to stay the same general size as your worshippers. Gods should also probably not really need most kinds of armor or artifacts, prefering to "grow" armor that is actually just a hardened body, especially since armor is cumbersome and slows you down. Weapons are a different matter, and most gods have some kind of special artifact weapon associated with them. Don't forget that gods can also get nifty syndromes: one Forgotten Beast that wrecked a guy's whole fortress was a giant crab that had breath that put enemies to sleep AND on fire.
The powers should also fade as a god's power base deteriorates - reduce the influence of their spheres, and kill some of their worshippers, and they become more and more vulnerable, and you can steal some of their spheres from them.