Hard drives with RAID here. No fancy software. I used to do sysadminning for a large public university so I learned some nifty tricks - most notably I found that I can use old (read: cheap) hardware with decently nice drives and a well-tuned setup to meet our throughput needs. We've found that eliminating the in-house backup/archive (with the cost of hardware in 2012) creates an overall win in reduced overhead for reprints and saved time and lack of confusion. Plus, Amazon's cloud has a cheap archival solution, so everything is backed up offsite.
We prefix the file with the job number, so if job 13145 is a reprint of 12189, the job ticket for 13145 will say reprint of 12189 and all I need to do is find the file that starts with 12189. Sort the files in the folder by name and this is trivial.
I guess we're not really archiving per se: we just add drives as necessary (and replace as necessary). Our costs are quite insignificant and our persistent cloud backup means that even if the building burns down, we lose at most one day of work.
We might be a unique case here, though, because we have many tenured customers and many of them have been using the same, say, logo for a decade or two. The trick to making it all work is organization: we use folders to organize what InDesign calls links - ie a logos folder. We do work for a real estate company that puts photos of realtors on business cards and fliers, and they send out cards with photos of individuals or individual photos of the whole staff. So we have a "Photos" folder for them.
Part of making this work is getting artwork to do things on production's terms: don't save a photoshop file, save a tiff. Don't save a .ai file, save a PDF (doesn't work as well for InDesign, but it's pretty rare for us to reprint an InDesign with no changes
. Then since we are Fiery driven, we can just take those files, put them in the Fiery, and use Impose to handle the rest.