Baking informaiton into clay tablets isprobably the best bit-per-year-of-rentention technique that mankind has invented. Not sure what's second best -- ink on archival paper?
[I don't count the recordings attached to the Voyager probes. We can't easily retrieve those.]
Oh goodness gracious no, if you're going to measure in linear bit-years it isn't even remotely close. It's hard drives, because the amount of bits stored on hard drives is just so staggeringly enormous it dwarfs the faint traces of fragments of bits and pieces of the ancient world that we've managed to barely save. Orders and orders of magnitude off, even if you decide to count things like raw scans of the ancient stuff as opposed to merely the bits of information in the text and the other handful of useful details like the carbon dating.
You need to do some sort of correction that nonlinearly accounts for lasting more than a few years.
I'm sure we can do better; we just haven't tested the newer alternatives over a long enough time span to be sure. Take a look, for example, at the Long Now Foundation's Rosetta disk:
They made a disk of sturdy, corrosion-resistant metal, micro-etched thousands of pages of text on one side, and covered the other side with a design of words spiraling into the center and getting smaller, until they were no longer visible with the naked eye -- meant to suggest at a glance what the disk was, and how to read it. The text is a record of thousands of existing languages, like a modern, souped-up version of the original Rosetta stone.
Acid free archival paper kept in a dark, fire proof box is to my knowledge the single best technology we've invented and easily at our disposal for long-term storage.
I think I might totally start 'printing out' photos I want to theoretically have available in fifty years and place them in a safety deposit box…
How stable would the various colors of ink needed for pictures be? I suppose you could also print out a separate B/W version of each color channel for later reconstruction.
Maybe you could print out a color calibration strip with known values, and then use that as a benchmark so you could reverse fading via software? Kind of like what NASA/JPL does so they can color-correct photos taken by planetary landers.
(I know that this isn't what the OP meant, but it's interesting to try and mitigate the limitations of the more common backup solution -- i.e., just printing the photos themselves).
Next to paper or parchment (mentioned below), there is a technique, that uses microform. Here in Germany a lot of long-term archival work is done with this material. The information is scanned and "printed" on microfiches. In one image, there can be stored a lot (i think up to 16) pages and a lot of images are on one roll of film. Then these rolls are transferred into special containers and put in an old mine in the German "Black Forest".
There are to date more than 28.000 kilometers of microfilm with round about 850.000.000 images. They estimate, that even in 500 years there will be no information loss on these images.
Very true. Acid-free paper has a expected life of over 1000 years. Think about how long paper documents like the Magna Carta, ancient illuminated bibles from the 700's, Shakespeare's plays have survived without special climate-controlled environments.
Also paper in bulk is hard to destroy. A stack of paper is pretty dense and can survive to some degree a house fire or flood.
If the room the clay tablet is in survives, the clay tablet survives. You can't say the same about hard drives and burned DVDs. Pressed DVDs are probably fine though.
The longevity of clay tablets would be biased by the limited technology of the time. Even engraved granite would be a better choice today, since we can easily machine it now.
[I don't count the recordings attached to the Voyager probes. We can't easily retrieve those.]