What Bregalad said.
Saving is definitely possible with any game as long as you have ROM space to code everything. The only limitation you might have are the save game files. SRAM is limited. So games like Tales of Phantasia, which already allow saving, can only have up to three at once and no more unless SRAM is expanded (Which is doable, but the main debugger people use mirrors it incorrectly so it can't work, but it should run correctly if they're saved in the new space).
All it takes is a little bit of coding and figuring out what absolutely needs to be saved into the file. Along with adding the menu and stuff of course, that's probably the hardest part out of the entire thing.