How important is the GRE for top engineering schools in the US? I am wondering how important is the general GRE exam for top 10 schools in the US in engineering? Do they use it as a factor to admit students or it can be only used for funding or none/both of them?
For engineering, the GRE is used primarily as a screening tool—and very weakly, at that. Having excellent letters of recommendation and a strong transcript can very easily overcome weak GRE scores, while a perfect GRE score won't save a candidate with a weak transcript or bad letters. Also, of the sections, the math section is probably given the most weight by admissions committees in engineering, since it's viewed as the most relevant.

As for funding, the only reason I could see the GRE being used is to "verify" English-speaking ability for teaching assistantships. I've never heard of the GRE being used to determine research funding.