To answer your question, no: all schools of reasonably well-known merit require a GRE. Shopping for schools that don't is only harmful. I am guessing your mindset is simply wondering if within, say, the top 100 programs there might be exceptions, perhaps because the test is a financial burden, but no, the GRE is the standard for admission. It's not the only important factor, but every school will require it. I've heard it described as a "sanity check" to make sure the student's abilities pass a check relative to what the recommendation letters and transcript advertise.
To flip the coin, imagine a school that doesn't require the GRE. Why not: what's wrong with it? Does it let students in who would have performed terribly, and risk a remedial first year? Does it let students in who are likely to drop out and simply don't fund them? Is it just really lacking merit? I would be extremely leery of such a school.
Regarding the TOEFL, the situation is simple. It would be foolish for a university to not make sure incoming students speak English. Even if you are sure of your ability and don't have the time to study or the money for the test, you should be leery of going to a school where there's a pretty good chance your classmates will include German, French, Japanese and Mexican students who don't actually speak English and went to the only school that admitted them after they failed the TOEFL.
On the other hand it is of course very important that you can pass. It would be miserable to marginally fail but not be able to teach a course effectively (which is how you pay for grad school in part) or collaborate with peers.