In the European Union we have a "Common European Framework of Reference for Languages". In practice all language certification programmes have one of those levels associated to them (ranging from A1, the most basic, to C2, the most advanced), so that it is possible to establish equivalences between common tests. This allows me to, say, determine if my A in the (life-time valid) FCE exam is worth more or less than a 8.0 in the (short-lived) IELTS exam.
This however doesn't help the student that wants to have an exchange program outside the European Union. I heave heard rumours that, e.g., the Cambridge exams in English aren't accepted in the states, but that could very well be FUD.
What are the most universally accepted certifications in English?
As always, it helps to be specific: - what kind of exchange program? - what is oversea? USA? Canada? Japan?
In the US for a PhD program generally TOEFL and GRE is required, and most cases cannot exchanged to other certificates. I don't know Master programs, but I would assume similar or same certificates are required. Since exchange programs are much more limited, and I saw a really wide range of people doing them, I am pretty sure that there are programs that do not require any certificates or very flexible.
In Far-East the universities are generally more flexible. Beside TOEFL, TOEIC is also a popular English test, but many have heard about IELTS, too.