Currently you can sign up for Green Bangkok WiFi which is provided by any "truewifi" access point. The problem is that you are restricted to 64kbps, which is just about enough for checking email and very light browsing.
A few coffee shops offer free wifi in the central Sukhumvit area. Larry's Dive on soi 22 has free WiFi, as does German Beer House on soi 11. A few other pubs also have free wifi, although it is questionable whether you'd want to bring your laptop to a night out of drinking.
If you are in Thailand for a while, you can sign up for faster True WiFi access by purchasing a True SIM card from any 7/11 and registering for an EDGE/WIFI package. http://www.truemove.com/eng/product/package/sms_mms_gprs.htm
You can get 30 days of GPRS/EDGE/WIFI for 450 baht. It is a reasonable price to pay, since you can use the EDGE connection wherever there is no WiFi coverage.