While it's unlikely you can get megabytes worth of data printed out (which would require a very high-resolution printer, and the equivalent scanner), it's quite feasible to print kilobytes worth onto a single piece of paper. There are various utilities which allow you to print binary files onto paper, with the equivalent functionality to scan them back in and reconstruct the original file.
One such tool is Twibright Optar, which from the description, "fits 200kB on an A4 page". It's possible to increase the data storage density using a higher-DPI printer, although you should note that it may affect data recovery in the future (see the reliability section in the above link; you could also overcome this with a few error-correcting encoding methods).