If you're talking about something like a medical or law degree, it's a bad idea to study abroad. You'd need to pass licensing exams in your home country, and you wouldn't get the right preparation abroad. Why study American law if you want to practice in India or China? Why learn English-language terms in medicine or American tax issues in, say, accounting, when you need to know the right medical terms in your language or the tax issues in your own country to be an accountant there?
Many other disciplines, though, wouldn't involve any problems. You'll need to check on which ones would require country-specific study and which wouldn't.