What all triggers the game to save?

Obviously, you can save the game manually at points of interest, and it saves for you whenever you get out of your ship. I also found out that it saves after you die (gee, thanks). Are there any other events that cause the game to be saved?

Using the save points and getting out of your ship are the only two ways I know of that will save the game. Aside from dying, as you've pointed out in the question, I do not know of any other ways to trigger the auto-save.

I found an article that confirms what I've said above.

During our time with the game so far, however, we’ve noticed that it looks like it creates a new save whenever you get into or out of your ship, and whenever you discover a new building or structure.

Source: http://twinfinite.net/2016/08/no-mans-sky-is-there-autosaving/