Yeah, Martyboy has a point. I wasn't specific enough in the last post, but I did mean what I said.
I've spent many weeks recenlty in both Taiwan and China and can definitely affirm that whilst having a degree is necessary for most jobs, it certainly isn't for all. For the best jobs in the highest ranked private schools and high schools required qualifications are usually "batchelor/masters degree or teaching certificate" interchangeable which I've been surprised to see on many occasion. Usually most adverts state (especially by the chain schools like Shane, Hess et al), that they need a degree but even for them, it's my feeling that they'll take a CELTA which is a rock solid qualificiation for teaching that's definitely equivalent in their book to a degree - it's only to show you can think, teach and have an education after all.
There's certainly no need to slash your options in half and rely on the piss poor wages offered by the majority of jobs in China, Thailand or god forbid Cambodia. In China the best jobs seem to be in Beijing, Shanghai, Tianjin, Guangzhou and Shenzhen at the moment.
Saying all that, perhaps the OP is just set on working as an ESL teacher for experience, in which case Martyboy's suggestions are down pat. I actually began teaching abroad by working in Nepal, followed by India and Pakistan, volunteering all three times. If it's only experience the OP is after, there are plenty of countries that would fall over themselves to have someone with a CELTA. The best thing I'd advise is to actually
write to several of the schools that regualarly post on the eslcafe job board. You could also try as Marty suggested at seriousteachers.com who will apply for a whole bunch of jobs on your behalf as well as tefl.com which also have a great job board section. Google isn't half bad either.
Persist and you'll find the job you want. Good luck!