With an Amiga A500, Action Replay cartridge (v1.5 or later) and memory expansion, it was possible to save a copy of the state of memory, much like a save state in an emulator. Were there any other systems that allowed save states to memory in a physical hardware / non-emulator environment?
For the Spectrum, the Microdriver (by Mirage) and the Multiface (by Romantic Robot) had the ability to save the state of memory, to cassette, Microdrive or the Spectrum +3's floppy drive. This state file could then be reloaded.
Later versions of the Microdriver also had the ability to do an uncompressed dump of memory, which was not intended to be reloaded. This was used as the basis for the .SNA file format used by early Spectrum emulators.
ZX Spectrum compatible Didaktik Kompakt had the ability built in - pressing
CAPS SHIFT, left arrow and right arrow together saved current state to the floppy (it used a few bytes on the stack, so it could fail sometimes).
Yes, two examples of these are the Final Cartridge and the KCS Power cartrdige for the Commodore 64. Both allowed the C64 to be "frozen" upon pressing a button on the cartridge and then via a menu the state of the system could be saved to either tape or disk. These states could then at some later point be re-loaded into the system and the C64 would then continue running from the original point of freezing.
There existed at least two such devices for the Super Nintendo:
The NakiTek Game Saver and Game Saver+.
I haven't seen a picture of the base version but the plus version is a bulky Super Nintendo cartridge with a slot on the back to plug the actual game cartridge into.
The difference between the two is that the plus version supports using AC power or AA batteries to retain the saved data after you power the SNES off and, according to this speedrun.com thread, improves compatibility with games like Star Fox.
(AC power is handled by plugging the SNES power supply into the Game Saver and then plugging its output lead into the SNES.)
Also according to that thread, compatibility varies and, because of the architecture of the SNES, you're likely to get audio glitches on restoring saves.
Clint from Lazy Game Reviews did an oddware episode about it.
There's also the Game Action Replay for the NES which is more or less the same idea, earlier and by a different company, and with a manual instructing you to remove part of your NES to get it to fit.
I've heard passing mentions of the existence of a similar device for the Gameboy, but I haven't had time to research that.
I remember now seeing an LGR Oddware video a few months back about an ISA card for MS-DOS PCs that allowed you to write save states. I think he demoed it on Crystal Caves but I don't recall what the product was called (probably another Datel product). I also can't remember if it saved to memory or hard disk... will try and find the video for more details.