Doom 3...well, you could pause in that game, but a lot of the time when you need to look up the code for something you have to look in your PDA.
Let me give an example: "Damn it, I need the code to this door, but I can't remember. Maybe this audio file will tell me the code to it. Let me just go into my PDA and...what the heck is that sound? Did my character just grunt in pain? Let me lower my PD-HOLY FUCK A ZOMBIE! QUICK KILL IT! AHH, I HAD MY FLASHLIGHT OUT! GO GO GO!" And then I would blast it with my Shotgun, but that is the best case scenario. I've gotten attacked by much more powerful things then just the plain old zombies and would often end up dead....and would have to restart the level due to my inability to save.