In today's tenuous market the give and take between buyer and seller can be delicate at times. Oftentimes the seller prices a home 7 to 10% above what market is. If you talk to almost any seller (probably even about your own home) they all think it is worth more than it is.
The buyer has three strategies. First they could offer far less than market (say $20,000 below) and hope to negotiate up. This is the typical "low ball" offer. Next they could come in at around 5% below market and have some wiggle room and present essentially a "fair" offer. If they really want the house now, and the situation says other buyers are in competition with them they could make a full price offer and close the deal. In the good ol' days multiple buyers bid up the price beyond the asking price. This would be the case in a strong sellers market.
The danger with the low ball offer is sellers are insulted. Agents are required to present all offers and in reality any offer is a "starting point." The problem psychologically for the seller is they feel low ball offer buyers are not serious and are just trying to steal their house. They often then resort to staying firm on their asking price and are not willing to reasonably negotiate from that point forward even if their house asking price was 10% too high.
Good buyers agents have the facts at hand to know what market should be based on comps which show average prices and days on market. This coupled with looking at competitive properties around the area also gives a good idea of what market value is.
As a buyers agent be careful with the low ball offer because from that point on your client might not even be in the game if they are indeed serious about wanting the house. As an advisor to the seller when getting a low ball offer, negotiate hard back to the buyers agent as the ball is in play and let the seller know that you'll run with this one and don't get their feathers ruffled. Just see where it plays out since an offer is still an offer.

Really great post, thanks much. My sellers aren't easy by any means these days.
When I reprresent Buyers who make a low-ball offer, the offer is always accompanied by a letter I write up, which explains where this "offer" came from. I will use the recently solds and actives, and just explain the average price per square foot etc. I think it really takes the "personal" away from the transaction. I tell my clients it is all just a numbers game!
When I get a rediculously low offer, I always try to keep my sellers from being insulted. One way which has been successful is to have a little fun at the buyer's expense and counter 30-40% higher than the asking price. That keeps the seller in good humor and sends a message back to the prospective buyers and the buyer's agent.
Gary - great post and wonderful of you to observe it from both ends. The key, as I see it, is to be empathetic to the buyer's desire to obtain a great deal but supply them with plenty of evidence regarding not only the house but the location (ie, neighborhood, school zone, etc) so that they fully understand what they are bidding on. Secondly, I always remind them that their "low" offer would be looked on a lot more kindly if they offered a personal letter explaining why they like the home and a bit about themselves so that the seller can be a bit more willing to understand the offer from their perspective.
As a listing agent, I remind my sellers that this is just a starting point and while it might not be a great offer, let's go back to the facts and research again all properties that have sold! I give my sellers monthly updates on all marketed properties in their area. However, with contract in hand, it's a great opportunity to power on the computer and sit and discuss what has sold....not what is currently still sitting active. This many times will bring them down to earth to consider the distinct possibility that the offer isn't as far from fair market value as they originally thought.