Which universities in the USA do not require TOEFL from an international student?

That would be almost none. If you don't speak english then you won't be able to complete the course work thus there would be no point in accepting you. If however you are from a country that speaks english aka England, Australia, etc. then I don' think you have to take it.

Now that I think about it though, if you really don't want to take the toffel some collleges offer English language programs the summer before you matriculate so that you can learn the language and be prepared. This may be a better option if your set on not taking the TOFFEL