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No. Use Bcrypt. Always. Bcrypt is backed by Blowfish, designed by Bruce Schneier. Go look it/him up. It's secure. MD5/SHA1/etc are not weak because they are cryptographically weak (though some are), it is weak because they are fast. SHA3, when it is picked, will still be a very bad choice because it too will be fast. So, why Bcrypt? Well, it uses Blowfish. Blowfish has a very slow key scheduling algorithm which basic…
Bcrypt is backed by Blowfish, designed by Bruce Schneier. Go look it/him up. It's secure. Well, yes, I trust the Blowfish cipher (and GP probably does too). The question is how we can be sure it isn't being somehow misapplied, i.e. whether the way bcrypt uses it opens some other hole. That's what I (and probably GP) would like to see an expert weigh in on.
First of all, none of this security even comes into play until after your password file is stolen, but your and jim's comments imply you believe that using bcrypt would somehow make an existing site less secure.