About Skyrim intro, the main issue I often felt, is that is just way too long, which is annoying if you are trying new characters. In comparison, Daggerfall, Oblivion and Morrowind, you can easily make bee line toward the end of the intro, see how your character is (specially in Oblivion and Skyrim, where light became more important) and restart if necessary.
Also, in Oblivion, you could simple save at the very end of intro, where it gives you a final chance to change your class and character, which was really useful for trying new characters.
Dragon Age Inquisition intro itself, isn’t bad, but the fact that the character creation happen in that weird green light is bad, since it make hard for you to see how clearly your character looks, meaning that you might choose wrong colors and only figure it out later and the whole intro sequence is quite long.
Earth Defense Force 4.1: intro is amazing - since drops you in a city attacked by lots of giant ants, with building crashing down, people running and you with some other guys and tanks trying to save everybody, soon as the game start, which put you in that b-movie absurd theme and aesthetics in a instant.
Wizard & Warriors (2000, Heuristic Parks): The intro of the game begin with dude telling you to find the “Mavin Sword” (which might be the least inspiring name for a magic sword) to fight against a evil mummy (or something), but for bizarre reasons, the very first you do in the game is going in way too long tutorial dungeon. Seriously, the intro dungeon take absolute forever - it keep going and going. By the end when you finally leave, the game does get a lot better, but this intro dungeon might discourage you to start a new game with a different party.