Which exam should I take?
Well, for most people, no exam is probably the right answer. I'd only recommend taking an exam if you need it for a specific purpose, e.g. for migration / education purposes.
IELTS, run by Cambridge, is the most popular exam with about 3 million test-takers every year. Most universities and countries that require proof of your English level ask for IELTS. The other Cambridge exams have an additional 2.5 million test takers per year, and exams such as First for Schools are particularly popular in schools all over the world. The Canadian government recently said that it would accept PTE (by Pearson) for immigration purposes, so this test has seen a spike. Many American (and European) universities ask for TOEFL, so this one is popular too. OET is popular for healthcare workers who need to prove their English level, and TOEIC is connected to English purposes.
There are many other exams out there too, such as ILEC for legal English, TEFI for hospitality English and BEC for business English.