Props to CyberAkuma for mentioning Space Ace and Dragon's Lair. I was thinking precisely the same thing about the button-reflex sequences myself.
You know what I hate? Juggling in fighters. Not so much in 2d fighters, because they're not supposed to be realistic, but in games like Tekken and Virtua Fighter. Do you know how much force a standard lunging cross punch has? I'll give you a hint; it's not nearly enough to lift a 180 pound human off the ground for a whole second, nor is it even close to the force required to abruptly stop a falling 180 pound object and project it back upwards for any distance. Soul Calibur is okay, though, from what I've seen there are actually very few juggle combos in that game, although I admit I haven't been paying attention since SoulCal 2.
I hate the bosses-as-puzzles aspect. Nintendo is particularly guilty of that lately, with Twilight Princess, and to a somewhat lesser extent, Corruption. I don't want my opponent to have a specific vulnerable weak spot that I can just solve some movement puzzle to get to every time, where until I solve said puzzle they are completely invulnerable. I want to fight it out, to best the bosses by virtue of my own skill or planning.
Similarly, I don't want to be able to stun bosses. I want them to be competent warriors, who have a greater instinct to fight through the pain than to reload in the open. Shooting a man while his pants are down isn't fun or rewarding; it's despicable and cowardly. Granted that game protagonists are less interested in honor than they are survival and getting the necessary job done, and so it is justifiable to do whatever it takes however cowardly it may be, but it should not be treated as the norm, the expected pattern.
I also prefer games that have alternate solutions to problems that are 'supposed' to be solved with a certain tool or technique. Portal wins at this because of the one testchamber with the 'victory lift,' where you can actually project yourself up the lift way before messing with any other part of the puzzle--and they left that capability in the game on purpose. Props, Valve. Twilight Princess also gets to be on this highlight reel for the armored knights with the tower shields that you're 'supposed' to fight with a leading quick-draw strike. Tower shields are big but these guys are too professional to drag the shields on the ground; a well-placed bomb arrow can go under the shield and tag 'em in the foot, which counts as a valid hit. I can't tell you how frustrating it is to play a game where I reach an impasse, and then get a really good, creative idea to unconventionally get through it, but am barred from so doing because of an invisible wall or overrestrictive physics.
Waggle, too. In the words of Tycho, when it works it's great, but when it doesn't work it is goddamned infuriating.
More later as I think about it, possibly.