If you take prescription medicine or have a contagious disease, you're going to have to do a bit more research before you teach abroad. Some prescription medicine, such as birth control, is readily available over the counter.
Other medication that is normally available over the counter, such as sleeping pill, may require a prescription in some countries. However, medication, such as diabetes or depression medication will require a prescription. Nonetheless, there are people in similar situations and they've done it.
Medical Exam Needed to Get Visa
Many countries, especially those in Asia, require medical exams in order to get you a work permit or Asia. Some countries will flat out deny you a visa if you have any disease, while others are more flexible.
Korea requires a medical exam, but due to pressure from Amnesty International has said that they won't deny visas based on the outcome of the medical exam. We'll see if that actually happens. Some teachers with Hepatitis C have said that they were able to get work permits. Others have called the Korean embassy and have confirmed that this is true. Keep in mind that while technically they aren't supposed to deny you a visa it could happen, especially if you have a more serious disease such as HIV or AIDS. For more info about blood tests and travel visit
HIV Travel, you'll find info there are tourist and work visas.
China has a medical exam, but teachers there have said that only having TB and HIV or AIDS results in denial of a visa.
Japan and Indonesia don't require medical exams, so you could consider teaching there as well.
Before Arriving
There are a couple things that you can do to make the move easier. First, talk to your current doctor. They may be able to recommend a doctor or clinic in the country you're going to. Second, get the generic names of the medication you are currently taking. Lastly, fill your prescription for as many months as you can. Some doctors will give you a longer prescription that you can fill in advance if you prove that you are leaving the country.
You will still have to do research before you arrive in the other country. A good place for information is
Dave's ESL Cafe and the
Lonely Planet's Thorn Tree Forum. Thanks to the internet, you can connect with other people who are in the same situation as you are. People on these two forums are usually very helpful and may be able to recommend how to get the medication you need.
You should also tell your employer
before you arrive in the other country. There are a couple reasons for this. First, some employers will not want to hire you when they find out that you take medication and may end up firing you. I know that this isn't fair. However, this has been known to happen. It's rare, but it still happens, which is why you should be upfront with your employer. In fact, on some visa applications you are asked about prescription medication. Second, on the opposite end of the spectrum, your employer is a great resource of information and can help you get the medication you need.
After Arriving
Ask your employer to help you find a clinic, hospital or doctor. Some doctors will speak English, or at least be able to read and write English, especially medical terms. Others may not, so you will have to bring a translator with you. Often someone from your school will come with you.
Bring any useful information with you, such as the generic name of the medication and the name of your condition in the local language, if possible. Remember to be patient with the doctors and people who are there to help you. If you've gotten information off people from the internet and they live near you, you might want to try to meet up with them and see if they can help you.
Conclusion
In conclusion, there is a lot of information you can get from your doctor and the internet so that you are prepared before you go. While some employers will not be willing to hire you, most will and furthermore, they will be happy to help you out. The best thing you can do is be prepared. Don't be afraid to ask questions and find others who are in the same situation as you are.
Disclaimer:
With work casual becoming the norm, we're seeing more and more teachers taking things to the extreme. It's not uncommon to see teachers wearing jeans, tank tops, or trainers to work. While some people don't see anything wrong with this, other people believe that teachers need to dress more professionally. 
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