This is really the wrong question. A better one is: Assuming you don't trust it, how much work does it require to trust it?
I have saved a copy of the site and even hacked a bit on the code but I wouldn't send a new user blindly to the site claiming that it's forever safe.
For this purpose, I am hosting a minimal address generator that uses python at github.
It's much less code to read and if a change is made you'll see it in the commit log.
http://github.com/weex/addrgenThanks for writing some code to generate addresses. For me, it's true that I have to start out NOT trusting that the random number generation is without any flaws. But as a non-programmer of java or javascript, I must rely on the opinions of others more qualified to look at the exact lines of code creating the addresses, and who, hopefully, also understand the crypto and the libraries the javascript is using. I see mandatory security updates to the crypto libraries of python in my Ubuntu distribution regularly, but don't understand the implications for applications that make use of the libraries.
I'm reading some of the other members talking about generating the input to hash on the bitaddress.org site, as meaning that, it's better to sidestep my question about how the site creates random numbers and generate the string yourself with your own entropy, whether you do it as a "brain wallet" or not. I have verified that the site really does give the sha256 hashes of what the user puts in the text box.
I have been surprised of how trusting people on the forum seem to be of the address generation process for private keys in general, from any of the applications that do this. Especially considering that security experts such as Bruce Schneier have observed years ago that the US government most likely deliberately introduced standards for "random" number generation for elliptic curves, (Dual_EC_DRBG), such that the author of the standard (NSA in this case), was in a position to posses secret keys would make the "random" outputs, predictable, which would make the encryption trivial for someone in possession of the secret keys to crack. Here is the article
http://www.wired.com/politics/security/commentary/securitymatters/2007/11/securitymatters_1115& I understand sha256 itself arose from a nsa standard. I would think if anyone on the planet has something better than brute force to break that hash, or to break a random number source, it would be them, especially when they are coming from standards they themselves authored. I'd be really interested in hearing from any of the developers of bitcoin software that know all about these issues and have thought about their implications for the applications they write.