Usually, the director is the one who comes up with the idea for a video clip. but what if the singer himself comes up with the whole idea? what is he called then? Co-Director? (assuming there will be a director to do all the technical detailed shots)

Director assistant maybe? Though he would be more responsible of moving the shoot on and keeping up with the schedule. I expect director's assistant to handle things around in a realistic manner unlike the director who wouldn't compromise for anything.
Whenever producers influence the film, director's vision is already compromised heh, same goes for cinematography. From the book of Blain Brown a circle of confusion can be the measurement of the point of light until it becomes unacceptably big or it can be when couple of producers sit in a circle and discuss cinematography. I am a bit rude today heh.

A Director directs the production phase of the overall program. That person may also play other roles and will work in their Director's capacity during pre- and post-production.

The source of the idea is not necessarily a title at all.

You see this all the time in movie credits:

Based on the book by . . .
Based on the play by . . .

or something similar.

How about "Creative Inspiration: ..."?

What do you mean by 'clip'? If you mean a shot as part of a whole then he probably wouldn't get anything.

But you said "the whole thing" which I guess means a whole music video, for example. He would then get a producers title, depending on his level of involvement, or a writers title or maybe a "created by" credit.

I've never seen a credit for that person on a video.

On the old Star Trek series there was always a title, "Created by Gene Roddenberry." I've seen "original concept by..." and "original story by...".

But he is talking about a music video.

I don't see why he couldn't give whatever credits he wants on a music video.

He can do whatever he wants. But he asked what that person normally is called on a music video. And the credit list just isn't that long on a music video. If this is for someone's resume, they can put whatever they want on it. On a music video, people wear a lot more hats than on a a larger production. So they can be caterer / assistant producer / grip / driver / security / bug wrangler if they want.

thanx for the reply everyone.
well, if the person says: "do a video clip in the desert", then he probably won't get any credits for that (it's too general). But I'm talking about a detailed idea. for example: "the man start walking towards the girl, she turns around, giving him attitude...etc".
i think "original concept by" would be alright. "Director assistant" would be too much, coz he won't be helping the director during the production.

Remember when the boulder comes rolling out of the cave towards Indiana Jones...

Somebody wrote that.

Credits on music videos, as Keith says are generally limited to Director and/or producer. But the person who "Comes up with the idea" is basically the writer... whether or not they take the time to write it down. "Story by" is good for longer forms, or "Conceived by" might be good if the artist has the concept, sketches out the scenario, turns it over to the writer/director to flesh out the details.