I normally have autosaves turned off. Although I just turned it on to take a look at CivAssist. I typically do a manual save prior to a big event, like switching governments. I'm still kind of new to this game and I have trouble determining if I have enough infrastructure to support Republic. When you come out of anarchy with -100gpt because your army is too big, it helps to have a save to go back to. In my last couple of games, though, I have gotten it right and not had to reload.
Where an autosave reload would help me is when I start drafting citizens instead of hurrying production. I just want to see how much it would cost to hurry along that shiny new whatever and instead I end up with a useless 2hp rifleman and a ticked off citizen. URGGGG. I wish those buttons were bigger!