Several mediums for geological timescale data storage have been proposed, such as
special glass based storage devices that are written once using two collimated lasers to make small structural (and thus refractive index) changes to the glass in small areas inside, and use that to store digital data.
The problem is that long term data storage is very... UNPOPULAR.
Everyone wants to be able to update the data in realtime, because of reasons, (some benign, some not..) and geologically stable data storage does not permit that. As a result, most data is stored either on flash memory (due to its high access rate), or on mechanical magnetic spinny disks still. Flash memory has a data shelf life of something like 10 years. It is basically the storage of charge states inside a crystal matrix, that can slowly discharge over time, resulting in data loss. Here's a primer on the tech.
http://computer.howstuffworks.com/flash-memory.htmMagnetic spinny disks you probably already know about, and magnetic hysteresis and other sources of bit flipping on the platter, are well known, and mitigated in a wide variety of ways by many different disk manufacturers, but the high density of the data on the platter makes them poor choices for seriously long term offline storage.
Not even CDR type disks are appropriate for archival data retention, as the dyes used to make the disks degrade chemically over time, and have a data storage life no greater than 20 years or so.
Basically, all the mainstream storage systems are not geared toward data retention in the event of a major decline, and the vast, VAST majority of digital data will be lost inside of a human lifetime if such a decline happens as a result.
You can blame the invisible hand of capitalism for that, along with modern business's insane fixation on being able to destroy and replace data in place for PR reasons. If humans can destroy the data quickly and easily, you can be sure as shit that mother nature can as well.