Bargaining
type of negotiation in which the buyer and seller of a good or service debate the price and exact nature of a transaction
Bargaining, also called haggling, is common in many countries, such as most of Asia, Latin America and North Africa. In other places, it may generally be used only for large items with no fixed price, such as buying a house or a used car. However bargaining is possible in almost any flea market or tourist shop anywhere. In such places, if you don't bargain, you are almost certain to pay more than necessary. Vendors expect a bit of bargaining so their initial asking price is considerably higher than they hope to receive, which in turn is higher than the minimum they could accept and still make a profit.
This article is about cultures where bargaining is common. In some other places it may be possible to ask for a discount, but there the nominal price is close to what you will pay and your first suggestion should be reasonable, perhaps the price you hope to get.

By all means bargain hard and try not to get cheated, but do not expect too much. You are a visiting amateur going up against a professional on their home turf. Just holding your own and getting a reasonable price will be an accomplishment; do not expect to achieve some miraculously low price. Against a pro boxer, almost anyone would be justifiably proud just to leave the ring on their feet; hoping to win the bout would be foolish and hoping to score a knockout utterly ludicrous.
Don't get upset if you pay somewhat more than a local would; that is quite normal in many areas. Even getting "cheated" in a local bazaar, perhaps paying $25 for something a local could buy for $10, is often better than buying it in some overpriced airport shop. It will usually be cheaper if you have even basic bargaining skill, and buying in the bazaar puts money into the local economy, rather than giving it to some large company or, in some places, helping crooked officials line their pockets.
If possible, try to buy in areas where there are many vendors and competition may bring prices down. In an example from China, one traveller reports finding some lovely silk shawls in the only store at a well-known scenic site, beating the price down down from ¥250 to ¥100, and thinking he had done reasonably well. A few days later he found the same shawls in a nearby multi-vendor commercial area with an asking price of ¥80 and bought a half dozen at ¥55 each. He felt a bit foolish but did not feel he had been robbed since back home those shawls would likely have cost at least the equivalent of ¥350; even a naive tourist paying ¥200 is not being robbed.
Consider your priorities. If you are bargaining over some silk item that would cost $200 back home, it may not be worth worrying about whether you pay $20 or $25 in Thailand. If you make good money and are spending a substantial chunk of it on a trip, then it makes no sense to waste a half an hour to save $5; your time is worth more than that and you have plenty of better things to do with it during a trip.
Also consider the vendor's situation. Sometimes the amounts you are arguing over are just a pittance to a traveller from a relatively rich country, but are quite important to someone in a poorer country who needs to make a living off the tourist trade. An amount that is large to you may be huge to the vendor. In some cases, for example, a big sale might mean the difference between all the vendor's children going to school this year or just the boys.
See the Shopping article for some alternatives that may let you avoid bargaining.