I'll use Far Cry 3 as a primary example since I'm playing it right now.
a) Make Quicktime events go and die. When a scripted even occurs right after a cut-scene and the words "Mash C" appear, do the developers really, honestly think it's fun? Is it supposed to be immersive, this mashing of a key? Is that what my character would do if really attacked by a shark, mash the hell out of random key? Which, usually, is used for the 'crouch' action. Am I crouching at the fucking shark? Crysis 3 was also really annoying for this. "Oh, long cut-scene, I'm gonna put the controller down and watch ... what the hell? I have to suddenly spam X? No, wait, wait ... argh."
2) Don't force scripted encounters where the player HAS to do X, Y, and then Z for arbitrary reasons. So I'm playing Far Cry 3 and the island queen or whatever the hell she is has me take a drug. Next thing I know, I'm having to fight a giant monster with a bow and arrow. I actually hate the bow and arrow and never use it. I want my bloody guns back. It's like some kind of boss battle in a different genre, I'm having to run around this small area, dodging magic ink balls, while attempting to shoot it in the head with arrows. Absolutely stupid sequence.
c) Random vehicles that I will only use once, just for this level, and which I have to learn about on the fly. No, thank you. Killzone 3 was bad for this. Most of my deaths came not when I was actually SHOOTING STUFF but when I was doing these vehicle levels.
8) Let me retain control of my character while I'm being talk at by an NPC. Far Cry 3 does this stupid ass thing where I can control the character's vision a TINY bit with the mouse but it's all floaty, like he's high on painkillers. The hell is that about?
I like freedom and versatility. I like side mission that feel important yet aren't like "kill random pirate captain X with a knife while he's peeing". I don't mind being on a ride but I want to be able to move around a bit while I'm on that ride. The game should be controlling the EVENTS, not ME. Let me control me.