BBUs on RAID cards. Yep.
Caching for storage controllers and the like. Yep.
Maybe even in the drive itself. Yep.
But everything else will need larger capacity, which I'm sure will come with one company's technology or another.
Surely a killer application would be pure and simple, however. Press the power button on your laptop, or even allow the battery to die, and it has a permanent suspend which isn't power related at all and can be resumed years in the future as if nothing had happened.
I'm sure we'll also start to need a "reset" button, because if something crashes like that, you won't be able to just power-off and let the BIOS sort it out!
But if they can operate in DDR ranges and they can be made in memory chip sizes, there's little reason not to use them, and end up with true zero-power suspend without a hasty "give me a moment, let me just write all that to disk" forced procedure. We all know Windows cheats here and turns the screen off then churns the disk for several tens of seconds afterwards while it ACTUALLY shuts down / hibernates.
And surely one of the main uses would be much more important - DDR3 speed recordings of sensor-data which are permanently stored as soon as they hit the RAM, even if the power fails. Black boxes anyone? You could record much more detail, much more quickly, much more resiliently, and keep every speck of live data that was churning through it, than something like Flash, disk, etc.