Well, first one must settle on whether 666 or 616 is the number of the beast. If the "number of the beast" is actually 616, then the entire premise goes out the window since the assertion is that each double set of bars represents a 6. That would mean that the two center long bars are either a 6 or a 1. And if people are looking for something, they will find it. One can claim that the word "giggle" has the number of the beast!
That said, one can find numerous barcodes that do not contain enough digits to make either number of the beast, but then you can make any other numerology number out of them.
Here is one that dismisses that urban legend:
(This comes from the CD by Elly Nieman, Circus Princes)
And I'm sure that you could find more on any trip to the grocery store. I just picked up a can of beans from the cupboard that didn't have a single 6 in it!
Even though the question was about the claim of 666 in barcodes, if you are interested in the history of barcodes and how they work, you can check out this "How stuff works" article. This webpage states that The UCC (formerly The Uniform Product Code Council, Inc.) is responsible for issuing product numbers, specification, etc.
If you are interested in barcodes and their development, this page has a link to a PDF paper on the subject.