A Tale in the Desert.

Well, if you can find it anywhere, there is the 1987 game The Seven Spirits of Ra:
http://www.mobygames.com/game/seven-spirits-of-ra

Also, if you can consider them RPGs in any way, there is the Tomb Raider series.

Would Darksun count as Mesopotamia?

Serious Sam!! ;)

My favorite location in Diablo 2 was Lut Gholein in act 2, but I think that's more of a persian theme

Dragon Wars for Mesopotamia, maybe. Mesopotamian gods in the game IIRC.

Sorcerers of Ur-Turuk.. sort of.

For that you would need other people.

It's neither a RPG, nor a PC game, but if this is no hindrance: "Eternal Darkness - Sanity's Requiem", a Horror-Adventure for the GameCube has several scenarios, including Persia (Mesopotamia), France, Cambodia and the USA.

It may not be what you're looking for - but it's a great game!

There's the Prince of Persia series, and Al-Qadim

But they take place a few thousand years too late.

We need computer and console RPGs with a little more variety in setting. They exist, or have to exist in PnP form, but not that I know of in videogame form. I'd also like one based on pre columbian america: Mayan, Incan, Aztec... all that.

Not a RPG, but Age of Empires 1. Also Age of Mythology (kinda)

This is a really good question.. I've been racking my brain but all I can come up with are RTS or Sim games..

Why do Greek and Norse mythology seem to get so many games based on them when the similarly rich Egyptian mythology seems to hardly have been touched..

I agree. That would be a cool scenario, too.