Since Sony own Insomniac Games, and the fact that Marvel's Spider-Man was an overwhelming success selling over 13 million copies, fans can expect there will be some kind of sequel.
There is no doubt that Sony and Insomniac Games are cooking up some form of sequel behind the scenes, and according to former Games Informer news editor, Imran Khan, they already are. Khan said during the latest Kind Funny Gamescast video that "I know too much about [Marvel's Spider-Man 2], so I can't speculate too much".
Imran continues and says that while players of the first Spider-Man might think that it will still be some time before they receive a sequel, "I think a Spider-Man 2 will come sooner than we think". This is promising news for Spider-Man fans are a sequel is definitely most welcomed. What won't be appreciated though is if Sony and Insomniac re-skin the first Spider-Man and just sell it back to fans as Spider-Man 2 with no new improvements. The sequel will have to feel new, more mechanics, more suits, new enemies etc.
I think it's safe to say that Spider-Man fans would rather wait more time for Insomniac to create a whole new game than receive a sequel that feels like a large DLC.