What does the advertised, or "list" price of a house really mean with regard to how much you should offer? It's certainly a clue to how much the seller wants for the home—but it's never the last word on the matter. Both the market and the individual sellers' predilections make a difference in whether the seller expects (or should expect) the eventual sales price to go up or down from the list price.
Don't believe the price tag. In the end, it's the market—that is, the level of other buyers' interest in the house, and their view of how it compares to other available houses—that rules.
In a hot market, with lots of demand for houses and prices on the rise, sellers commonly take an approach that seems counterintuitive. They list their houses at an artificially low price. Why? It helps make sure the maximum number of buyers come in to take a look, so that a bidding war ensues and the price goes sky high, even higher than they might have realistically listed the place at.
Of course, other home sellers may set a more realistic, or even optimistic, price.
In a cold market, where houses are moving slowly and demand is low, it's more common for sellers to set the list price that's meant to be "just right," so as to neither scare away potential buyers nor feel stuck if only one offer comes in at list price.
Nevertheless, some sellers in slow markets choose to set the list price on the low side, just trying to get potential buyers to come in and take a look. They figure that if the place really is a bargain, more than one person will bid, and the price will eventually get moved upward anyway.
Then there are the sellers who set their house list prices on the high side, either wanting to set a starting point in negotiations (not a good idea), or because they're blind to what their house is worth. Sellers tend to have difficulty believing that their house has dropped in value (which can happen dramatically after a major market correction).
Sometimes, the fault for overpricing a home lies with an inexperienced or unscrupulous real estate agent, who "bought the listing"—that is, convinced the seller that he or she could get a higher amount for the house despite what other agents were saying about how the place compared in value to other properties.
It's perfectly legal in most states for the seller to reject a full-price offer, or indeed any offer (unless the reasons are discriminatory). A seller who is expecting higher bids may do just that.
The exception is that in certain states, sellers must accept a full-price, "clean" offer—that is, one that comes with no contingencies, such as the sale being conditional upon financing or approving the results of a home inspection. But most buyers feel it's important to include contingencies into their offer, for good reason.
In the end, it's up to you (with the help of your real estate agent) to decide how much a house that you like is really worth—and how much you're willing to offer for it. Base your offer price on such factors as:
Putting it all together, you'll need to arrive at a number that's high enough to get the seller's attention, but low enough that you won't feel buyer's remorse for having overpaid. If there's competition for the house, this may be your only chance to impress the seller. If not, and you come in low (but not insultingly low) the seller may be willing to negotiate, and will send you a counteroffer.
A final hint: Although many homebuyers tend to think in multiples of five, that is, of offering either $350,000, $355,000, or $360,000, there's no rule that says you have to do this. If, for example, you know that another buyer is interested in the same property as you, and you think that person is likely to bid $360,000, you could always bid $363,000, just to set yourself apart.
For more information on getting to know your local real estate market, looking carefully at houses, finding the house that's best for you, and making an offer, see Nolo's Essential Guide to Buying Your First Home, by Ilona Bray, Alayna Schroeder, and Marcia Stewart.