What universities are recognized by USA universities? I just completed my bachelor of Electrical engineering with first class honors at The University of Western Sydney. I am now thinking of doing a phd in one of the good universities in the USA.

When I look at the minimum entry requirement for graduate admission in MIT, Stanford, UCB, ..., they all indicate that I should have a bachelor from a recognized university. How can I know the university that I completed my undergraduate degree, is recognized by these American institutions?
There is an official list of accredited US institutes of post-secondary education, the database of accredited post-secondary institutions and programmes, but according to that page, the Department of Education does not maintain a list of recognised institutions worldwide.  Instead, there is an educational NGO, the Council for Higher Education Accreditation, that maintains a list of accrediting bodies that are recognised by its member organisations (which include Stanford and UC Berkeley, but not MIT), the Database of Institutions and Programs Accredited by Recognized United States Accrediting Organizations.  The institutions recognised by the member organisations are the institutions accredited by one of these bodies, which are national in scope.

As a state university, the University of Western Sydney is accredited.  For other institutions with less international visibility, rather than look up this information yourself, it is better to contact the HR department of the institutions to which you apply to get their direct judgement on whether that institution is recognised by them.