In the comments on The Keshik Feigned Retreat Ambush, Lingaholic related a story --
I've also had some more or less scary experiences in the developing world. I think the one I most vividly remember was back when I arrived in Saigon, Vietnam, back in 2009. I decided to catch a cycle-rickshaw, or whatever you call them there, and I asked the price beforehand for a ride that would've taken something like 10mn. I knew the usual price went by US$1 (around 15,000 Vietnamese dong I think). The driver responded, cheerfully, "You pay what you want. No worries. Just pay any amount you want." I kind of insisted in knowing how much he charged (rather than firmly making my offer), but just got the big smile with the same response.
I decided to take the ride, and after getting driven around to shops owned by his buddies, and pressured into buying some crap, I finally arrived to my destination. Disembarking the cycle-rickshaw, I tended a $1 bill to the driver, and said thanks. He then looked at me and said, "No. You pay me $15. This is the price for the ride." At that point I basically laughed and categorically refused to pay him the exorbitant sum he asked. He continued, increasingly more aggressively, to insist on me giving him the equivalent of US$15. After about 10mn--which felt like a long time believe me--where I basically just stood in front of him replying "no" over and over again, he started shouting "I going to kill you. No joking. I kill you right now."
At that point I started freaking out a little bit, but luckily it was midday, and there was a lot of people around, as well as curious bystanders (all of them Vietnamese, none of them really interested in helping either of us, but most seemed to sympathize with the driver). At that point I basically tended him the equivalent of $5, which is still hugely overpriced, and walked away, never looking back.
Lesson learned that day: always agree on a price before taking a taxi/rickshaw ride.--
Bold added by me -- that's precisely why people do it. By making exorbitant demands, they usually get something more than normal.
Two pieces of advice -- first, if you get caught up in one of these, don't discuss with them -- just hand them something and leave. And laugh a little instead of taking it as a serious argument.
Once you get caught up in a "serious" conversation, they know they've got you. When someone asks for money like that, I go, "Haha, that's a good one. Here's [whatever]" and then walk away just like you did.
The line, "Come on dude, I live here" is pretty useful too (even if not necessarily true).
For more complex transactions, a very simple piece of advice that helps a lot -- write down numbers. Take out any scrap of paper, write down a number on it, and write TOTAL in caps. Circle it.
This isn't necessary for a short taxi or motorbike ride, but very useful when buying multiple articles of clothing, or getting some package tour. You'll often get extra charges tacked on or the price changed, but people seem to be unable to do it as ridiculously if you've written numbers down. If it's a multi-element transaction, break it down with numbers related to each item.
Also, you really don't want to pay beforehand, almost ever, in developing countries. Things go wrong too often. But yeah, a lighthearted chuckle and smile, along the lines of, "Hey, I don't blame you for trying, but c'mon man hah" is far more likely to get you out of there with problems than trying to reason with unreasonable and unscrupulous people.