Boy, now this is an area where a crystal ball could make a guy a fortune. Not having access to a dependable, accurate crystal ball, one needs to rely on the advice and experience of their Broker. Many factors come into play in the initial offer. Some say always offer 10% less. Unfortunately, this route could end you up in second place on that competitively priced "perfect" home for your needs. And, second place is no fun.
Things to consider are:
How long has the property been on the market?
If a new listing, how competitively priced is the property? I've had situations where the home was so well priced, multiple offers are received within days. In this situation, offering a few hundred dollars over list made the difference in owning versus second place. In other situations, it's obvious the property is $20,000 overpriced and a lower offer can be justified and submitted with documentation to back the offer up.
Current market conditions can play a big factor. A Broker active in the local market knows what's going on in the market and can advise you accordingly.
The best advice I would give in what to offer the Seller is "get good advice and listen to it!" Too low of an initial offer could insult the Seller. Too high, and you may be leaving money on the table.