David Edelstein kind of loves it:

I'm not making the case for a movie like The Amazing Spider-Man -- only saying it's fresher than Raimi & Co.'s shambolic Spider-Man 3. (No, it can't touch Spider-Man 2, the best of all the Marvel pictures.) The new Peter Parker is Andrew Garfield, the glowering dweeb from The Social Network, and where Tobey Maguire was soft-faced and mild, examining his sudden, sticky excretions with an adolescent's wonderment, Garfield is high-strung and angry -- and those excretions don't come naturally. (This Peter has to build his web-jets.) Because a primal trauma must kick-start every superhero career, we've seen little Peter lose his parents (Campbell Scott as his scientist dad, Embeth Davidtz as his mom) in the prologue, and high-school Peter beaten up by bullies. His powers emerge spasmodically, twisting him in knots, his body with a mind of its own. The problem with the first Spider-Man was that whenever Maguire got into his suit, he transformed into a little video-game fellow swinging around an artificial cityscape, fluidity trumping realism. Director Marc Webb makes the flights more jagged, mixing up his angles and adding Spidey-eye views for the wheeee factor. At one point, Peter channels Ratso Rizzo: "I'm swingin' here!" You don't get that weightless, inhuman CGI vibe as powerfully.