If I'm the seller I would prefer to throw out a number. That way you can simply pad the starting point, coming down in price is much easier than going up.
If you are that much more concerned about getting the best possible price (or whatever) vs. getting a set number you actually want, then you should go into the negotiation with enough information to already know what the best possible price should be.
I once suggested a salary range from [thrilling for me] to [unbelievable] and was offered the high number. I never felt like I "lost" -- until of course a year later when we were all laid off in early 2001. Ah, the "dot-com era."
I suppose some people will always be haunted by suspicions their deal could have been better. But for me, people instantly accepting my high offer is not going to be a lifelong regret.