I voted 'slow down' because, imho, it serves to ruin the immersive experience of games more than any other feature.
Jaggies may look ugly, sprite flickering may grate, jerky scrolling may hamper gameplay at times, fogging on N64 was just plain funny, pop-up isn't a particular hindrance, colour clash was bearable and often worked around on the Speccy, etc. All annoying but tolerable to a greater or lesser extent. Slow down just kills the gameplay experience though.
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I really am surprised to see I was the only person who voted for sprite flicker.
I was playing some NES games for review purposes recently and some games are near enough unplayable because the flicker is so bad.
I just haven't played many games with sprite flicker. Or if I have I don't remember. Slowdown however is something that tons of console games have from every era.
If you use a black and white television the sprite flicker is not as noticeable.
If you use a black and white television the sprite flicker is not as noticeable.
That's interesting. I wonder why that is?
Being an Intellivision guy, the limitation that annoys me the most is the 20Hz frame-rate of old Intellivision games using the built-in "Exec" operating system.
This translates into a game-cycle that updates only 3 times a second, causing the game to run slow--even at their fastest speed.
The worst of all symptoms tied to this limitation is that the controller is polled slower than what would be good, making the game feel sluggish.
 dZ.
Being an Intellivision guy, the limitation that annoys me the most is the 20Hz frame-rate of old Intellivision games using the built-in "Exec" operating system.
This translates into a game-cycle that updates only 3 times a second, causing the game to run slow--even at their fastest speed.
The worst of all symptoms tied to this limitation is that the controller is polled slower than what would be good, making the game feel sluggish.
 dZ.
This is indeed a very common complaint I hear about Intellivision games. Thankfully, homebrewers like you have better options today to program better games. 
Slowdown can be annoying but I've seen it used to great effect in shmups - particularly in boss deaths (e.g. Radiant Silvergun). As long as it is occasional it doesn't break a game.
But nothing makes a game more unplayable than flicker. Nothing worse seeing hardware being pushed too far - and that's why it gets my vote.
I'm baffled at the Nintendo controller hate - I find that odd - I get on with most controllers. I can see how some ports of games to the GC would be problematic though - but playing something like Super Monkey Ball on the GC shows how superior the GC pad can be with the right type of game. The only controller issues I have is when the developer doesn't let you configure your own controls - nothing worse when you keep getting fire and jump mixed up in one game because they are the opposite of another game you have been recently playing. I also get annoyed with games that don't let you reverse up and down in a 3D game.
The DC controller's dpad is abysmal.
I also hate the fact that paddle controllers have gone - too many broken Arkanoid ports because of that - though some Wii games have used the remote as a paddle pretty successfully (Bit Trip Beat for example).
Lack of high score saving is something else I will find irksome - Darius Gaiden on Saturn being one culprit that stands out.
Finally - and I find it odd it isn't in the list - are load times. They break a game for me and I have returned games because of them (Bust a Move 4 on PS1 for example). Lengthy load times would be number 2 on my list.