Tuk-tuks are the adventure vehicle for getting around town. They're cheaper than taxis but not always the cheapest deal in town. The quality of a tuk-tuk ride can be a pretty intense experience and varies wildly from driver to driver and from city to city. Here are my suggestions for two major cities.
In Bangkok: Fare negotiation was a huge hassle. There are loads of hustles going on, so be careful, particularly around tourist hubs (the Grand Palace, Wat Po, Hualamphong train station, etc). They'll catch you about half a block from the hub, then tell you that it's closed because of a Buddhist holiday (except for what's far from where you are). In addition, you might negotiate a price, and then, half a block into your journey, they'll try to swing you to a jewelry store. Tuk-tuk drivers can get free gas for steering tourists to jewelry stores. If you like playing these sort of games, then have fun. In Bangkok, I stuck to metered taxis whenever possible (and don't let taxi drivers tell you that their meter is broken).
In Chiang Mai: Metered taxis are not to be found, so you'll have to rely on songthaews (spelling varies), or tuk-tuks. Songhhaews are little red flatbed trucks that have a couple of covered benches in back. They're good for getting around, but you're at the whim of where they're already headed, and things can get pretty crowded onboard. Tuk-tuks are far more reliable and less scammy around here, and they'll get you right where you're going pretty quickly. If you want to tour some of the more remote wats, you can frequently negotiate a pretty fair price for the whole day. They can get more expensive at night, particularly when you're headed to (or from) touristy restaurants and bars.