I have included the TOEFL requirements of the ultra elite below. MIT makes the TOEFL optional
Penn/Wharton
TOEFL
The Test of English as a Foreign Language (TOEFL) is required for all international applicants whose native language is not English. You may waive the TOEFL if you have earned an undergraduate degree or master's degree in an English-speaking country or from an institution in which English is the language of instruction; applicants must provide evidence to support the waiver. If your test score is more than 2 years old (from the date of the exam to the date of application arrival), you must retake the test. Administered by ETS, the TOEFL is offered throughout the year at test centers worldwide. Wharton only accepts official TOEFL scores sent by ETS.
Wharton's TOEFL code is: 2926-02
Stanford
All applicants to the Stanford MBA Program who do not have an undergraduate or graduate degree from a university at which the primary language of instruction is English must take the Test of English as a Foreign Language (TOEFL).
Chicago
Q: Can I have the TOEFL or IELTS waived?
A: An international applicant, however, is exempt from the TOEFL/IELTS requirement if he/she has earned an undergraduate degree or post-graduate degree from an institution in which English is the language of instruction. An applicant is also eligible if he/she is a citizen or permanent resident of a country where English is an official language. Applicants should indicate the exemption in the application where indicated.
Harvard
Candidates from non-English speaking countries are required to take the TOEFL and /or IELTS, according to the following guidelines:
Candidates who received their bachelor's degree from an English-speaking university are not required to submit these tests (i.e., they are exempt).
Candidates who received a master's or Ph.D. degree from an English-speaking university are strongly encouraged to submit the TOEFL and/or IELTS.
The Admissions Board discourages any candidate with a TOEFL score lower than 267 from applying.
We strongly urge students from non-English-speaking countries to take the Test of Written English (TWE), now part of the computerized TOEFL.
TOEFL or IELTS scores more than two years old will not be accepted.
Northwestern/Kellogg
Who is required to take the TOEFL?
A valid score for the TOEFL is required for international applicants whose native language is not English AND who have not received a university degree in one of the following countries: Australia, Canada (not including Quebec), England, Ireland, New Zealand, Scotland, South Africa and Wales. Please note that TOEFL scores are valid for two years.
Does Kellogg offer TOEFL waivers?
Although we strongly encourage candidates to take the TOEFL based on the criteria listed in the previous question, we will grant exemptions for candidates who graduated with an undergraduate degree in which English was the only language of instruction AND who have worked three consecutive years within the last five years in an English speaking country (see previous question for list of countries) where business was conducted in English. Please note that the Admissions Office reserves the right to request a TOEFL score if additional information is required to assess one’s English skills.
Candidates who fulfill the requirements for a TOEFL exemption must indicate such in the Additional Information section of the application. Candidates also must submit documentation from the university that all courses were taught in English.
Columbia
International students whose native language is not English must take the Test of English as a Foreign Language (TOEFL). You may be exempted from the TOEFL if you have received a degree from an institution whose official language of instruction is English.
MIT
TOEFL
Am I required to take the TOEFL?
No. The verbal sections of the GMAT will be used to evaluate your English language ability. Applicants who do take the TOEFL may report their scores to help demonstrate their English language ability, but it is not required.