We are usually in Thai speaking churches but on occasion, we have had the opportunity to worship at an English-speaking international church in Bangkok. I don't know enough about any of them to give an unqualified endorsement, although at the ones we have had occasion to visit, the experience has been positive on the whole. Check out their websites for more information, directions, and worship times.
The Evangelical Church of Bangkok (http://www.ecbbangkok.org) is located downtown on Sukhumwit Road, Soi 10. I am told that it is quite international interms of worshippers and overall feel. Friends have told me that they have been appreciated the more-or-less expository preaching at ECB.
Christ Church Bangkok (http://www.christchurchbangkok.org) is an Anglican church in downtown Bangkok, in a large building that looks like it was imported straight from England. Decent sermon when I visited a number of years ago on Easter.
Chaengwattana Community Church (http://www.cccthailand.org) is a standard evangelical type church, with a very American feel, located in northern Bangkok on Chaengwattana Road (not far from old Don MuangAirport)
International Church Bangkok (http://www.icbangkok.org/) describes themselves like this: "ICB's morning worship is in a traditional Presbyterian style. Evening worship is sort of InterVarsity meets casual contemporary. We are a church where anyone (Christian or non-Christian) can come and draw close to Jesus in an atmosphere that is safe, honest, and open. We come from a wide variety of countries, cultures and ways of thinking about just about everything. What we have in common is a love for (and an interest in learning about) Jesus. He is at the center of everything we do."