This post by Talysman is pretty timely, as I've been reviewing how I run AD&D vs. how I run GURPS.
I'm sure I've mentioned this before, but I run die rolls two different ways in my two different games:
Pretty much everything except damage and player-facing effects rolls (or a roll to see who is affected) are secret. To hit, defenses, resistance, etc.
Sometimes I'll roll wandering monster rolls in front of everyone just to make a point about people spending a lot of in-game time in a dangerous place.
My players are too good at figuring out stats from data derived from successive combat actions and then making plans based on those odds. That's not something I want for my GURPS game.
I roll almost everything out in the open. Only rolls specifically called out by modules as needing to be secret are rolled in secret. I announce AC, roll damage, roll initiative, saving throws, etc. all in the open. For me, it's part of the fun of taking an AD&D vacation is getting to relax and play it all in the open.
Back in the day I used a DM screen. These days it sits flat for use for tables only. It's all in the open.
Do you play different games with different approaches to die roll secrecy?