Actually I'm not sure how much this is a great travel tip for travelers in Bangkok. I've never used the motorbike taxis myself, but have thought a few times of giving it a try. Perhaps you've made the experience and could write a comment to it...
When traffic slows to a crawl in Bangkok and there are no mass-transit alternatives for your destination, by far the fastest mode of transport is a motorbike taxi (or in Thai, motosai lapjang). No, those guys in the pink smocks aren't biker gangs; they're motosai cabbies. They typically wear colorful fluorescent yellow-orange vests and wait for passengers at busy places. Prices are negotiable; negotiate before you ride.
For the adrenaline junkie, a wild motosai ride can provide a fantastic rush. Imagine weaving through rows of stopped vehicles at 50km/h with mere centimetres to spare on each side, dodging pedestrians, other motorbikes, tuk-tuks, stray dogs and the occasional elephant while the driver blithely ignores all traffic laws and even some laws of physics. Now do the same while facing backwards on the bike and balancing a large television on your lap, and then you can qualify as a local - though you might die in the process. Imagine your loved ones arranging to ship your dead body home from Bangkok because you took a dangerous risk you were warned not to.
The overwhelming majority of motorcycle taxis do not travel long distances, but simply shuttle up and down long sois (side-streets) not serviced by other transport for a fixed 5-20 baht fare. These are marginally less dangerous, especially if you happen to travel with the flow on a one-way street.
The law requires that both driver and passenger must wear a helmet. It is the driver's responsibility to provide you with one, so if you are stopped by police, any fine is also the driver's responsibility. This is worth bearing in mind when you hire a motorbike or moped. Make sure that if there are two of you, the hirer provides two helmets not one. When riding, keep a firm grasp on the seat handle and watch out for your knees.
Motorcycle accidents are brutally common, and many (tourists and Thai alike) consider transportation of this sort to be inherently hazardous. Motorcycle taxis in Bangkok should generally be avoided except as a last resort.
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Based on a work at Wikitravel.org & Traveldudes.org.