I usually use save states either in games where there is not a save function baked in, or when I'm playing a game that does have a save function but it is limited (Final Fantasy's save points, for example).
If I'm playing a game where there is no save or a password system that would take time to take advantage of, or a game where I can't immediately get to a save point, and something comes up that will force me to stop playing, I save state, shut off the game, go do my things, then come back where I left off.
I admit there are certain points in certain games where I feel compelled to save state, just in case I get completely shitstomped, but those are the fewer-and-farther-between use cases for me. Not only did I grow up on the NES and already have a lot of these games mastered, but I don't like the idea of save scumming my way past a hard part... I get a kick out of beating it 'the normal way,' somehow.
Just farming endorphins like a good lil' gamer.
I do try not to use save states on anything CD-based, though, because the game state is not read from the disc the same way as it would be for a cartridge, and some several emulators over the years have had problems with that (particularly ones that will run files that are either cartridge-derived or CD-derived, PCE-CD, Sega CD, et al).