Try as you might, bargaining is often a 'they win, you lose' situation
The actual price can be up to ten times less than the starting price and it is when you hear these quotations and know the correct/fair price and have to spend so much time and effort to achieve something close to it, is when you get so frustrated. If so count to ten and move onto the next vendor and make it clear why you are doing so. This almost always happens in locations that have a large tourist footfall. Many traders are honest and getting a little ripped-off is just a fact of traveling - after all, you can afford it, so don't get too enthusiastic or disillusioned.
This subject still needs more explanation as it's often misrepresented in guide books and by other travellers, who sometimes assert that every price is negotiable. This is a half truth, almost always applicable to souvenir sellers, taxi, rickshaw etc. drivers and a few others that become clear when on the road, but not always in other situations depending in large measure on the nature of the country you are in.
Prices are always going to be higher in a sellers market than a buyers one, so if you need something like a long distance ride in a taxi or a souvenir where there is much competition don't get too enthusiastic and waiting to be approached rather than approaching works wonders. Equally the western mentality of asking a price and retreating if not interested can be considered as an insult. Bottom line is if you don't have serious intentions of buying - don't ask the price and certainly don't start negotiating, doing so will only invite hassle.
It goes without saying that the problem facing the traveller going from town to town and country to country is knowing when they are being asked a fair price, and thus hitting the right balance between politely paying up and aggressive posturing to establish if they are being ripped off. To complicate the matter further is the notion of a fixed price, as locals will bargain as well. The best approach is to visit a few stalls and get a feel for a price (walking away will always lower a very high price) and if a stall owner is reluctant to negotiate, you can assume you have a fair price. Likewise quotations that start with the word 'around' or 'something like' are certainly far off realistic.
Conversely, if buying a 'daily item' like a bottle of water, ice cream, bus ticket or similar, and you find yourself in a bargaining situation, where maybe the seller has dropped the price after your hesitation, don't bargain. These are not items anyone bargains for and you are simply being ripped-off. In the event tell the vendor to get knotted and walk to another seller. However let's keep things in perspective, in experience it is only in areas with a high tourist volume that absurd prices are asked and everyone seems keen to add their own 'little commission'.
As stated, tourist souvenir sellers (especially African curio sellers and mass tourism areas of Asia) in particular always ask an inflated price. These are often so whimsical that you can't really have a rule of thumb. But even when buying curio (African wooden carvings) and similar, you can bargain too far.
A case in point observed was watched a couple off an overland truck in Malawi buy a wooden carving which the seller wanted the equivalent of US$15 for. It was a nice piece and probably took about two to three days to make. Generally the going price for an item like this would be around US$10 which the seller soon dropped to (he seemed pretty desperate for business). However the couple then spent the next 5 minutes getting him down to US$8. There are plenty of other examples e-mailed to the site and this sort of behaviour is disgraceful and goes on all the time (see the 'value of your money' write up in the following section). Rather than giving to beggars, perhaps consider being a little generous when dealing with individual souvenir and fruit sellers (not large stalls).
Overcharging on transport, private or otherwise, is common place in many countries and there is little you can do about it except be philosophical. Nobody likes being ripped off but if that's the price, you have to pay it and if it is a little inflated then why should a few dollars extra ruin your day/trip? That said, always arrange a price before you get into a taxi or any other mode of transport: ask a local if unsure. Some drivers are very good with 'as you like' or 'cheap' type sayings, mimicking bad English. Be firm - don't get bullied. If there is no meter, agree a fair price before you set off.
And finally... One argument often heard is that travellers have an ethical duty to bargain prices as low as possible, otherwise they risk triggering inflation that will eventually put goods out of the reach of locals. If you think hard about this, apart from a few extreme cases, you'll only see this sort of statement to be obnoxiously self-serving.