Yes (edit: almost). Open the Javascript console (F12 if you use Chrome) and type
String = function(){alert('bang!')};
You can rewrite (edit: almost) everything in Javascript - even in the global window context! evil.js is a library that uses this trick to rewrite as many native objects as possible.
Needless to say, this is very dangerous. I have executed the above String code, and since writing it, I have caused more than 520 Javascript errors (and I have seen "bang" several times). Internal objects are used universally, and you should not modify them if third-party code relies on them in ways you are not aware of. This is one of the reasons Prototype.js has lost its popularity, because its extension of its own objects often worked against the expectations of other code.
Edit: Actually the false statement that absolutely everything can be overwritten, as indicated in Bergi's answer . Editing done inline.
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