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I want to move an object to a specific point on the screen. (Specifically, wherever the user touches, barring any collisions that may interfere.) What OpenGL ES call am I supposed to use for this?

A: 

You need to use a equivalent method of gluUnProject, which transforms from screen coordinates to world coordinates. There is one implementation specific to iPhone here.

Basically, it uses the modelview and projection matrices to do the transformation.

Matias Valdenegro
Nice pointer. However, Cocos2d for the win!
Moshe