What are renowned universities famous for?

I am asking this question in general and to satiate my curiosity that has arisen after I read about QS world university rankings. Then, to make my point clear, I know Harvard University, for example, and if we consider Harvard university, then what is it famous for? I heard much about it, but I am not very sure why it is so famous and prestigious. Your opinions?

I ask you to name any university that you know and write briefly why it is considered good or best. Yes, I am aware of university rankings according to specific areas.

Then, I would like to know about following universities: Stanford University, Massachusetts Institute of Technology, University of Cambridge, University of Oxford, University of California (at Berkley and at Los Angeles).

You are free to add any university from the world that you think is good or best or prestigious, etc. and tell me why do you hold your very opinion? Your thoughts are appreciated.