In most places the basic requirements for entry level teaching positions are a degree plus a TESL/TEFL certificate.
Europe might prove more difficult not only because you don’t have a degree but also because EU passport holders are always preferred.
China is still quite relaxed with the rules of requiring teachers to hold a minimum degree. However it will largely depend on the employer and their specific job requirements. In theory you only need a degree if you want to work in a university or want a residence visa. Having said that it is also true that employers in China are starting to list a Bachelor's degree amongst the qualifications required. This does not mean that you have no chances of getting hired without a degree, it simply means that you may not have the pick of the jobs.
Vietnam, Philippines and Indonesia are also countries where you can still be employed without a degree.
Some countries have an agreement with Japan which entitles their citizens - aged 30 or younger, to a working holiday visa regardless of whether they have a degree or not. Check with your embassy to see if your country is one of those who have undersigned this agreement with Japan.
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