They haven't finished filming the first one yet, but Sony seems so sure that Marc Webb's reboot will be so successful that they've already set up the sequel to be released on May 2, 2014. Either they're really pleased with the shooting so far, they've read James Vanderbilt's follow-up script and squeed with delight, or they're trying really hard to kick Marvel Studios around a bit with their own character. Or all three.
I'm confident in Andrew Garfield's take on the character (read Quint's interview here) so I'm sure he's game for another go-round. A quick sequel turnaround's not unprecedented for this franchise either - SPIDER-MAN 2 came out 2 years later. I'll chalk this up to Sony's confidence in the new film. Either way, Spidey fans should be elated.