NOTE: The following article contains spoilers for The Amazing Spider-Man.
The "sequel tease" is, by now, as obligatory to superhero movies as masks and capes. Either directly before, during or after the ending credits, an extra scene fades into view revealing some new piece of information - maybe a character thought dead is alive, maybe the villain for the next film makes an appearance, that sort of thing. The modern trend started with Batman Begins' climactic reassurance to mainstream audiences that the next movie will feature a villain they'd actually heard of, but it was cemented in Iron Man when Samuel L. Jackson's Nick Fury stepped out of the shadows and declared that the superhero genre was about to evolve to the next level.
The Amazing Spider-Man (just to reiterate - a God awful film) concludes with probably the most perplexing "the hell?" example of such a tease yet, whereas The Avengers big reveal likely baffled anyone not steeped in Marvel Universe lore. Even die-hard fans can't seem to figure out what Amazing Spider-Man is trying to tell us. Dr. Curt "The Lizard" Connors is sulking in his prison cell during a thunderstorm, when a mysterious figure steps out of the shadows, his face hidden, clad in a long black coat, futzing with a hat and speaking like someone doing a late-period Nick Nolte impression. He's come to grill Connors about Peter Parker - specifically, how much he's told him about his father (in the new continuity, Richard Parker and Connors were OsCorp scientists who invented the super science gobbledygook that turns Peter into Spidey and Connors into the Lizard before dying alongside his wife under conspiratorial-looking circumstances). Connors tells the mystery man to leave Peter alone, after which, the man seemingly vanishes from the room during a thunderclap.
So ... who was that? I don't know, and I don't think the moviemakers know, either. The Amazing Spider-Man is said to have undergone extensive reshoots (which may or may not have involved excising what were supposed to be big story-changing plot points and/or setups for the next movie) so it's wholly possible that this was supposed to be a specific character who's now been re-edited into a mystery-man-to-be-determined-later. Most of the early speculation made the obvious conclusion that it had to be Norman Osborn (re: The Green Goblin) who is unseen in the film but repeatedly said to be dying of some unspecified illness that Connors' shady genetic-engineering research was supposed to be curing. But now, according to The Lizard himself, that's apparently not the case.
So, who was that? Or, rather, who will the makers of The Amazing Spider-Man Part II decide he was? Here's a set of my best guesses, based on what little is seen/heard of the guy in question, the circumstances of his appearance, compatibility of theoretical comic characters with the world of the film and other factors.
An early and comparatively minor nemesis from the early days of Spider-Man continuity, today mostly notable because he ties in to the origins of the Green Goblin and because his relationship to Norman Osborn (he was Norman's college professor; they became friends and went into business together before Stromm went bad) is kind of ironically similar to Peter Parker's relationship with educator/father figures turned evil like Curt Connors and Miles Warren. He appeared, briefly, in the original Sam Raimi Spider-Man movie as the scientist in charge of the project that ultimately creates The Green Goblin. His presence here would make as much sense as anyone else, though it's unlikely he'd warrant a teaser of his own.
Spider-Man continuity has more mad scientists kicking about than a Transylvania TED Talk. Spencer Smythe is a scientist contracted by J. Jonah Jameson to build remote controlled anti-Spidey robots called "Spider-Slayers." Eventually Spencer got his ticket punched, but his son Alastair picked up the mantle and kept the robot-making dream alive, eventually mutating himself into a "human" Spider-Slayer.
I'm putting this on here pretty much exclusively because the shadowy figure seems to "teleport" in and out of the prison cell during lightning, and because he's a fan favorite character in a similar vein to The Lizard. Electro has one of the best simple/brilliant/goofy origin stories in comics: Maxwell Dillon is an electrical-engineer who gets struck by lightning while working on power lines and, instead of killing him, the jolt grants him electricity powers which he uses to become a criminal. Sadly, it's a given that a movie would probably try to come up with something more convoluted and "realistic" than that.