You guys are all oversimplifying why various movies were successful/unsuccessful. There are a ton of different factors involved.
Frankly, I think the stink of Batman and Robin is overstated in why Batman Begins wasn't overly successful at the box office. Obviously it was a big part of it, but there were many other things at play. I think there wasn't a whole lot of excitement about ANOTHER Batman movie at the time, the general perception was that the movie was a prequel (the idea of a reboot was pretty uncommon at the time), and the marketing didn't emphasize flashy CGI set-pieces that were becoming increasingly common at the time.
There wasn't a ton of flash or sizzle to it. It kind of had the perception of "oh, they're making another Batman movie." Then, people saw it, and realized that it was a great movie, and completely unlike what they had previously experienced as a Batman movie, which obviously contributed (among many other factor's such as Heath Ledger's portrayal of the Joker and untimely death) to The Dark Knight's Massive success.... It's also important to remember that $205 million domestic is nothing to sneeze at. Underwhelming for a Batman movie? Sure. But it's not like the movie was a bomb, and most superheroes would give their left nut to have one of their weaker movies gross that huge.
The difference between Spider-Man and other "reboot" scenarios is that they didn't stop making the series the first time around because it wasn't successful. They were just afraid that ballooning costs making the movies less profitable in the future, and the original talent were becoming disinterested. It was a pre-emptive strike, really.
Anyone who thinks that Spider-Man carries with it a Batman and Robin like stigma is grasping at straws. Look at the Box-Office numbers and Rotten Tomatoes reviews for Spider-Man 3 vs. Batman and Robin or Superman IV. Those movies were crushed critically, and massive failures at the box office. Spider-Man 3, despite what some fanboys will try to tell you, was neither.
I'm very interested to see what kind of numbers The Amazing Spider-Man does, because frankly, it's in a unique situation.