And some level, this becomes impossible.  Consider the case of the famous Pentium floating point bug: you not only need to conserve your models, your data, your parameters, your packages, all external packages, the host system or language (say, R) as well as the OS ... plus potentially the hardware it all ran on.  Now consider that some results may be simulation based and required a particular cluster of machines...

That's just a bit much for being practical.

With that said, I think more pragmatic solutions of versioning your code (and maybe your) in revisions control, storing versions of all relevant software and making it possible to reproduce the results by running a single top-level script may be a "good enough" compromise.  

Your mileage may vary. This also differs across disciplines or industry.  But remember the old saw about the impossibility of foolproof systems: you merely create smarter fools.