Bangkok has gotten a lot easier to get around since the introduction of some mass commuter systems over the last several years. Between the express boat and the trains, you can get to most of the major sights of Bangkok quickly and easily. The trains can be quite crowded during rush hours, and are best avoided during these times.
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Bangkok Transit System
Better known as the Skytrain, the capitol's first mass transit system is a quick way to get around. The system isn't very big, with only two lines, so it probably won't go exactly where you going, but it can cut a lot of time from a cross town trip. A three-day unlimited use ticket can be purchased at all stations and many hotels for just 280 Baht (7.27 USD). Included is a tourist guide and system map. Several stations now also have tourist information centers with qualified English speaking attendants to answer your travel questions. Information centers are located at Siam, Saladaeng and Taksin stations.
Most Thais now use the term "subway" although the operators tried to get it known as the "metro". The system was opened in 2004, several years after the Skytrain. While the Skytrain is elevated, the subway is completely under ground. The Skytrain was built as an elevated system to save cost and because many believed that an under ground system would be prone to flooding, but when residents saw the impact the elevated system had on the city, the outcry insured that future mass transit systems would be built under ground.
Airport Express and City Line
The City Line and Airport Express opened in 2010 to connect the new airport to the city center. It's useful to note that there are two separate services using the same tracks: The Express line runs without stopping between the airport and the City Terminal near the Petchburi subway station. The City Line is a commuter service that runs from the airport, but makes several stops between the airport and City Terminal, and proceeds through the City Terminal to the Phaya Thai Skytrain station.