Doing a similar job to the taxi is Thailand's ubiquitous tuk-tuk ตุ๊กๆ). So named because of the sound of their engine, these are motorized rickshaws and are popular amongst tourists for their novelty value. They are occasionally faster than taxis in heavy traffic as weaving in and out is easier, but generally about the same or slower. Without any luggage, 3 people can fit into one fairly comfortably - it's possible to fit more in but it gets a bit cramped. Fares always have to be bargained for, and it is sometimes possible to bargain tuk-tuk drivers down to less than the taxi flagfall of 35B when they make good value. Most times, they offer no savings over a taxi, except perhaps if you're good at bargaining and can speak good Thai. The initial price they quote is likely to be well over the going rate, but it's easy to bargain it down to a more reasonable one if you know roughly the equivalent taxi fare.
It's essential to bargain the price with tuk-tuks before getting in. If you only ask after the ride, it's likely to end in a request for an ridiculous fare which can obviously lead to an unpleasant situation.
Just like taxi drivers, the tuk-tuk drivers mostly come from the rural northeast of Thailand and don't have to undergo any training (some will not even have passed a driving test), so don't be surprised if they sometimes have no idea where your destination is. A subtle point to remember when in one is not to rest your feet on the rail near the drivers head, as doing so is extremely disrespectful towards the driver.
As tuk-tuks are open-ended, they expose passengers to the high pollution levels in the middle of Bangkok's roads and offer almost no protection in case of an accident. There is theoretically a ban on new tuk-tuks as they are so noisy and polluting, but it doesn't really seem to be being enforced at present. Nevertheless, many of the local residents are not too enamoured with tuk-tuks nowadays and, were it not for their popularity with tourists, the days of the tuk-tuk on the streets of Bangkok would surely be numbered.
Though they are initially popular with tourists, most people seem to stop using tuk-tuks fairly quickly. They have something of a reputation for taking passengers to an entirely different destination than the one they requested, and it's not undeserved either. This alternative destination is invariably a a type of shop, usually a tailors. They get paid a commission from the shop just for bringing you there (though whether they admit this to you is another matter), and this often takes the form of cash and/or a free petrol fill-up in a nearby station. If you find yourself in this situation, there's not much you can about it, except take a brief look in the shop, come out and wait to be taken to your proper destination. It's not a good idea to buy anything in the shop, the prices are marked up significantly (30% +) to give extra commission for the driver and profit for the shop, so they'll be cheaper elsewhere.
Remember too that tuk-tuks are no cheaper than taxis, and if you're offered any trip for what seems suspiciously cheap (e.g. 10B, 20B or even free), they have to make money somehow. You can be 100% sure this fare will be subsidised by either visiting a few clothes shops or as part of the infamous gem scam. The plus side of this is that you can often get to your destination quite cheaply, providing you're prepared to put up with a little sales pitch on the way. Some people even recommend telling the driver you know what he's up to before you get in, and you don't mind going to a couple of shops for him to pick up commission in exchange for a free ride ! Given that most tuk-tuk drivers English is extremely limited though (not extending much beyond 'Hey you ! Where you go ? You want tuk-tuk ?'), how well this plan will work if you can't speak Thai is debatable. On the other hand, it's not unusual for the driver simply to drive off after receiving his petrol voucher and leave you in the middle of nowhere - not a nice situation if you are a new arrival.
In general, the same rules apply to tuk-tuks as to taxis if you don't want any problems. Don't take ones that spend all the time parked in tourist areas, don't act like you've just arrived and problems are be unlikely. In addition, avoid offers from tuk-tuks for 'shopping trips' or 'sightseeing tour' for 20B/hour or similar, as it ends up wasting a lot of time. In the evening, when the shops are closed, is the best time to take a tuk-tuk if you want the experience.