Animations for actions you perform often in games that waste your time and become boring. Quicktime animations for combat moves in action games, slow motion or forced bullet-cam for critical hits/kills/jumping a car etc, digging up stuff in Risen games.
A lot of these things should be optional, they become old really fast and serve only to annoy and most of them aren't even cool to begin with.

I must admit I'm also sort of an in game stalker. Checking out where the npc's go in GTA, Oblivion, RDR, Skyrim.
However when you get a mission to follow someone I usually hate it. Probably because you have to stay exactly so many feet behind. Yes a car stopping 50ft behind you at each intersection is not suspicious at all...

In GTA I also used to park somewhere and listen to the radio looking at the day night cycle. RDR had some pretty sunsets too.

Flying around in Arkham City.

Collecting Golden Film Reels in LA Noire - had to do it to get the trophy, but seriously?? What's the point?

Not really unnecessary as it's neccessary to get the trophy - but it felt like a pointless inclusion and bored me half to tears.

Why did you do it then?

Reading the mind of all NPC in Golden Sun 1 and 2.

I do all the things in the OP + (only thing I can think of atm) getting all the coins on screen before moving forward, Super Mario

Moving a fat plumber around.

Collecting coins in Mario
Random Encounters in Final Fantasy.
Loading Times.Metroid Prime had this shit covered in 2002

Those random cell phone calls people give you in GTA (sidemissions). Currently skipping most if not all random sidemissions in Red Dead.