I really like the trains in Thailand... fairly efficient, very cheap, and as JohnAx mentioned, there's a station right in front of the airport. From there, you can take trains to Chiang Mai, Nong Khai (near Vientiane, Laos), and Ubon Ratchathani. Or, go into the city to catch a train headed south.

I'm doing VTE-BKK-SIN by train soon, via the "jungle route" in Malaysia; BKK-SIN is probably the more interesting part of that route, so you might want to look into it. I hear the Malaysian interior is quite beautiful; will post a report in a few weeks.