Mike Gorz, the Director of Creative Services at Y&R Chicago used to have this diagram taped to his office wall. There's a lot of truth to this little sketch, and you'll find yourself often wishing clients understood it better.
But if this is the triangle clients should understand, here's another one agencies should have a grasp on.
Hopefully, none of us are in this business just for the money. That's a lousy reason to get into advertising. But sometimes agencies stick with a client that they don't like and who continually kills good work simply because they pay well. Presidents and managing partners do this do avoid laying off employees. It's not ideal, and it's probably not a long term relationship, but it keeps the pink slips away.
A lot of pro bono work is done with the "we like you" and the "you let us do great work" legs. It's the symbiotic relationship of a pro bono account.
I don't know if there's a magic formula for getting all three. If you stumble upon it, please let me know. But I think it's enough for us to realize that these are the reasons we do work for clients. And if none of them are present in a relationship, there's really no reason for it to continue.