I used to play without it, but I remembered I could use that!
Though, It still depend on the game.
I use savestate when I can't save but have to stop playing, in case NDS battery dies while in sleep mode, I won't lose progress (because SuperCard DSTwo is really hungry on battery and I often have the console depleted when I open it).
I also do it before or while doing a hard boss battles if I can't manage to do it the normal way after few tries. instead of losing time, I "cheat" on surviving. But I prefer doing savestates than using cheatcode for infinite HP.
Not all game or consoles let me do that, so when I can't savestate I just play safe, don't hesitate to go far away back to find a save before doing something dangerous/boss/etc.
About skyrim picking locks, I also always save before doing anything that could fail. It's not like it's cheating, the game let you save whenever you want. why not use it?
I also tend to switch save slot or keep few of them when I can (mass effect, skyrim, etc. lot of save slots,)
Just in case I did something wrong, I can reload an old save and do things differently. but I rarely reload a very old one unless I've really mess it up.
I can also abuse savestate to try different scenario. (Xenoblade and the multi-branch face-to-face cutscenes, save try one, reload try another one, reload try another until I see all possible outcomes), this is only for the purpose of seeing everything the game has to offer without replaying the game from the start.