There really is no rule, but here is what I do for my clients to determine the best offer price. We carefully check out the comparables in the neighborhood and decide what the home's value really is. I have found that when REO's come out and if they are well-priced they receive accepted offers right away because of their pricing. Typically, at least in the beach areas, it is better to offer more than asking, if the home is worth it in order to win the bid. Ask yourself, is this the home I really want? Then, over the course of a few years that extra $10,000 you offered in order to win the bid is worth it. There are other savvy buyers out there, looking at REO properties just like you are, so you do have to be willing to offer a little more. Let me know if I can answer any other questions for you. I have successfully completed these transactions. It does take patience working with the banks, because of their heavy load...but in the end you usually get a good deal on a home you like.
James' answer is pretty accurate, especially for his location. In Orange County, CA., there are probably 4 different price ranges - Condos under $350k, which are frequently a little negotiable, Houses under $450k, which are not flexible at all, Houses between $450k and $750k, which are a little more flexible, and Houses over $750k, which become more flexible, the higher their price range.
That being said, there is no set rule of thumb, as all lenders are different, as are all listing agents. Just like with non-REO type listings, there are listing agents out there who try to tell the lenders they can get more money for their properties than another agent can - they typically price their listings a little higher, which usually means more flexibility as they have to start reducing the price after a month or two, if it isn't selling.
I will say that if you're looking for an average single family detached house, under $450k in the O.C., you should consider yourself fortunate if you get it for 5-10% less than list price. A good percentage of them are selling for more than list price.