What did Deities and Demigods teach everyone?
We learned that it didn't matter who or what you were- If you had stats you could be killed. I heard more than one anecdotal story of high level players hunting down gods for sport just because someone thought it would be cool to take Mjolnir from Thor's cold dead fingers.
So can you incorporate deities into games and not have them become a target? Sure. Step one though is don't give them stats. Keep them on a completely different level of the game than the players.
This doesn't mean that the players couldn't or shouldn't get to interact with these supreme beings of creation and destruction.
Some ideas on different ways to approach having a god in the game.
Treat gods like environmental effects. Much like when adventuring near a volcano, there will be different effects whether the players are at the base, on the rim, or within the lip of the volcano. Is the volcano active or dormant, it is erupting? Similarly, the god will have different effects depending on the proximity the characters have to it, as well as the mood of the god. While the players may be able to directly affect the attitude of the god (of course this depends on the god...), if the god is angry, the best the player's can really hope for it to get out of the way.
Have demi-gods act as the gods proxies. Here is an opponent the characters can kill, but in the end even if he is the "big bad" of the adventure, he is only a fraction of the power of the deity that spawned him. On a similar tact, the players can encounter someone cursed by a god, that can act as a major foil. Greek mythology is great for examples along this line.
There is no god. That's right one answer might be that everything the characters believe is a lie perpetuated to make people feel better about existing in a cold bleak uncaring universe. All those cleric spells are really just the other side of the coin as arcane magic.