I have not read all the responses and this is directed at the op.
Percentage-wise, zero percent is as low as am willing to go. Below that you are just dealing in negatives and imaginary numbers.
On a serious note, I find that typically, a slightly over-priced place can start as low as 20% below asking.
On a place that has an asking price that is supportable by comps, I would stay within 5-10% of asking (unless the buyer does not care if he gets it).
If the place is wildly over-priced (there are fewer now than a couple years back) then I will come in as low as I need to for it to make sense.
Typically, any offer needs to be supportable by comparable sales to be taken seriously.
Sometimes there is some non-obvious aspect that can make your lower-than-comps offer better (eg: it is all cash, the seller was charmed with your wife). The short sales are often an example of this. The patience they require costs money. The showing is generally tough because they are usually occupied with sellers or tenants.
Sometimes seller fear can make a low offer more desirable. However, betting on this is like betting on seller cockiness during the boom. Its not a good indicator of anything and is unreliable as to its predictive capactiy.
As a general rule, though, one should not base any offer off of anything other than market conditions. The comparable sales tell you what other people are willing to pay.
People who offer inappropriate amounts are as effective as those who ask inappropriate amounts.
