Certainly in the world. The US generally has by far the best universities in the world, pretty much uncontested.
http://en.wikipedia.org/wiki/Academic_Ranking_of_World_Universities
Berkeley is ranked number 3 overall worldwide, behind only two private US schools (Harvard and Stanford). In fact, UCLA, UCSD, Washington and Wisconsin are also ranked above the first public non-US university (Tokyo University). Cornell is also part-public and might count. The list looks biased towards big schools, but that should favor all public universities, not just US ones.
Well, firstly, those rankings are hardly infallible and they fluctuate quite a bit. You'll also note that if you look at them again, you're wrong about UCLA, UCSD, Washington and Wisconsin all being ranked above the first public non-US university as Cambridge University (ranked 4) and Oxford University (ranked 10) are both above them. In fact, if you look at the last six years of those rankings, Cambridge has ranked above Berkeley in three of them. You'll also find that if you look at other rankings, Cambridge actually ranks above Berkeley - take the THES-QS World Rankings for instance (which Hugh has linked for you) which serves to emphasise the subjective nature of the rankings (in fact, if you look at the wikipedia page you cited you'll find that there is a note stating that a 2007 study was done which found that the Shanghai results could not be reproduced from the raw data it was meant to have used and that there have been suggestions that the rankings were partially influenced by perceptions). Berkeley certainly is one of the top but I wouldn't say it is 'certainly' the best in the world.
It also depends on what criteria you're looking at for 'best' - are we talking teaching (which isn't recognised in the slightest in those university rankings and is far more important for an undergraduate's experience) or research? On both counts, I would certainly say that Cambridge gives Berkeley a run for its money - students are often taught one-on-one (or at most eight students to one academic) with what is widely regarded as the best mathematics undergraduate degree in the world (as well as very impressive faculties in other sciences, history, philosophy etc etc) and you'll find that Cambridge is the most decorated university in terms of Nobel Laureates (83 to Berkeley's 47), as well as having strong reputations for research in a diverse array of subjects.
