1) Poking holes in things ( tape, DVD, etc )
2) Magnets ( core memory, drum memory, tape, disks )
3) Circuits ( DRAM, NAND, etc )
Examples of all three of these still exist.
What's interesting about XPoint is it is literally a fourth form that has never been commercially available: melting a substance and cooling it quickly or slowly, forming either a crystal or amorphic solid, which then has different properties. We don't know what the substance is, but it's cool that we now have this 4th thing.
This is exactly how rewritable optical media works.
4) Delay lines. I would definitely not categorize these as circuits. The bits are stored as pressure waves in motion.
5) Electrostatic charge. Talking about the Williams tube. The bits are stored as residual charge on a phosphor surface.
Also, phase-change optical (as in rewritable CDs/DVDs).
Also also, printing stuff out at high bit-density with good ECC, and scanning it back in again.
Also also also, chemically encoded bits (as in the DNA-based storage that was demonstrated recently).
There are more, not in common use or very scalable (e.g., mechanical switches).
I think the problem with paper is thot it's not really part of the computer any more. You need a human to take the paper out of the printer, store it, and put it back in the scanner. At least with tape and optical, we have robots to do that for us.
Generally no amount of ECC will help the default failure mode of these.