The sole reason why Spider-Man 2 is much lauded over its predecessor is because it is more mature. Not because it had to be, but because it learned from its past silly mistakes. This one is mature, dramatic, symbolic, and has emphasis on the psychological aspects of it. Even though this flick is not without its silly little touches here and there, it behaves like a responsible elder sibling that makes its predecessor a Sunday morning cartoon. Spider-Man 2 is the best from the series, and arguably one of the finer examples in the superhero genre, but despite this, is also rejected by the more action-heavy. It's funny how they reject this installment but love the 3rd one which is, in my opinion, the least memorable in the series. It plays out like a wireless mouse soon to run out of batteries. Just like the previous entry, this too is quite self aware. The part where Peter Parker ditches his costume in a trash-can, everyone treats it as the end of Spider-Man. I mean, no one says "this must be a fake" or "it must be a prank by the local joker" or anything. It could be anyone's costume for all we know.
Spider-Man 2 has too much to offer than your regular superhero movies. I mean, this film was The Dark Knight before The Dark Knight. It's one of those "To be or not to be" movies where the protagonist / antagonist has to decide whether to live out the rest of their lives as a man or as a mask. Here we see Peter Parker get affected by the failing relationship between him and Mary Jane - well, practically with everyone - and this in turn affects his costumed second life, with his webbing running out and falling from buildings. Look at the scene where he tries to save a kid from a burning building. Even though he's a superhero, he has rejected the idea, hasn't allowed his alter-ego to surface in a long time, and because of this he's unable to break down the door and get affected by the flames. You are who you are as long as you think you are. Stop thinking, and you unbecome that person. Not that you become an entirely new person, you just unbecome that personality. It's like filling or emptying a glass of water. If you fill it, it unbecomes an empty glass, but a glass nonetheless - and vice versa. The same goes for Dr. Otto Octavious, who becomes Doc Ock, the new terror in town. His mask is a metaphorical one. Unlike Green Goblin in the previous film who can't seem to remember his maniacal phrase at times, Doc Ock has rejected his once civil and honest man lifestyle. When the webhead knocks some sense into him, Doc Ock goes back to himself - a sort of reverse of what happens with Peter Parker. Hence this is the reason why he says "I will not die a monster" before, well, dying.
Mary Jane Watson, as we get to know here, is a somewhat successful stage actress. She plays Cecily in the play The Importance of Being Earnest by Oscar Wilde. The use of this play, and the certain scenes we get to see from it, is somewhat symbolic, or a metaphor, to the main theme of the film; identity. In the play, Cecily is so fixated on the name Ernest that she doesn't seem to care whose face goes along with it; the man has to be named Ernest, that is all. Algeron, the dandy of the play, assumes that name and tries to woo her. Although he is successful, he gets caught - but Cecily forgives him anyway, for she has fallen in love with Algeron - even though she already had fallen in love with him, but through a fog. The ending of Spider-Man 2 is very much reminiscent of this, as Mary Jane finds out about Peter's both true self and of his secret identity, and seems to forgive him and wants to spend the rest of her life with him, come hell or high water... or Venom, Carnage, Mysterio, Sandman, Hob-Goblin, Black Cat, Rhino or any from spidey's colourful rogue gallery :)
The version I downloaded was 2.1. The ".1" means it's an extended version, with over 8 minutes of scenes cut from the sans ".1" version. Viewing this version is one of my most pleasurable experiences as a movie-goer. I recently saw the "Redux" version of Apocalypse Now, but this "2.1" beats the "Redux" by miles; not by the longevity, but by subtleness of it. The scene with Mary Jane and Peter Parker by the fence is further extended, giving us a deeper look inside the life of the latter. The scene is almost flawless. Tobey Maguire almost flawlessly captured the micro-expressions, making him more than flesh and bone. See, it's these little things that count. If that doesn't sound too grabbing, then at least you get to see J. Jonah Jameson pretending to be the wallcrawler in his office... with the costume on!
Alfred Molina, you will agree, gave one of the greatest performances in a superhero genre. Willem Dafoe was amazing in the predecessor, and Thomas Haden Church was muscular and strong in the successor, but both of them weren't 1/4 of Ock's tentacles. In my opinion, this is the greatest performance given in the superhero genre, villain or hero.
In conclusion, Spider-Man 2 is a damn great film, if you ask me. Beats the first one by miles. Also, it is one of the Big 4 of the superhero genre, alongside X-Men 2, The Dark Knight and Batman Returns.