I still don't use Save States for the most part, with exceptions. It feels like cheating when using Save states, so I end up just using the regular save files the game provides. Exceptions are games that use passwords, but even then I rather want to write down and enter the password (or screenshot it). Another reason to avoid Save states is, they can break over time when becoming incompatible and are not transferable to other emulators as well.
There is a game I am currently playing on and off on an emulator, which really badly needs some better saving mechanism, where I start considering Save states at the moment: Deception 3 on Playstation. It takes forever and multiple menu entries and clicks before ingame save file is loaded. Then saving isn't automatic and awkward in a submenu after and before each round only. Once I forgot to save (modern habits of autosave). Also each saving and loading time takes also some time. All of this would be instant solved with Save states.