No, it doesn't. Once the salt is large enough that you don't have several passwords hashed with the same salt value, there is absolutely no further advantage. Frankly, 64 bits of salt seems like enough for anything. Triple-salting sounds like a technique made up by an amateur who doesn't understand what salting is supposed to do.
Not quite the same application, but it would seem best to take a conservative approach and make your salts 128 bits because the storage required is so small - you are only storing one per username.
Right, but this doesn't make the search space 2^64 times larger, or anything of the sort. Once you've assigned a unique salt to every password, you're not getting any further benefits from salting. This is what the Mt. Gox owner doesn't seem to get, with his "triple-salting".
The NIST application involves generating keys from passwords, which you might do a gigantic number of times for every password to get unique sessions and so on. They're not talking about password storage. And even then, 128 bits seems like a huge overkill, which was included just because it's cheap, so why not. I don't mind 128-bit salts, but let's not promote that as some "ultra-secure" feature, which it isn't.
