Personally, nothing. Well, my pocket, I guess. But no covers protect the screen themselves -- well, I suppose the recent popularity of "flip covers" do afford some protection there; people use various screen protector sheets for that. Nothing stopping anyone from using those without a cover, either.
If the phone is so fragile you have to surround it with rubber bumpers and bulletproof acrylic, why does anyone want it anyway? I've had my Lumia 1020 for almost 2 years. One scratch; probably got that two days after I got the phone. Not a single scratch since, and nobody'd see that one scratch without tilting it in reflective light specifically looking for it anyway, since it's very tiny.
The last time I ever used a screen protector was for an old original-version Windows Phone back in the stylus days, and then because they didn't have fancy things like Gorilla Glass, and you were actually scratching as plastic stylus across it to use it. But I do remember one day ripping the stupid thing off; I wanted to see the screen, not some plastic thing with the screen behind it.
If you have to have a cover to use a phone day to day, the phone is designed poorly.
If you have to cover the screen with a protection sheet of plastic, the phone is designed poorly.
I want a smartphone I can use, not a device I fear breaking or damaging every time I pick it up or look at it sideways.