Well anyone who has seen the film will know that the reboot has focused quite a lot on the science/biology side and it got me thinking who could be adapted to really suit this vibe. My first thought was the Scorpion. I mean when you think about it he could be perfect but unfortunately that probably isn't going to happen as he has been used in the video game (which is meant to be in continuity with the film franchise).
So who else does that leave? Well to me that only leaves a few more that could really fit in with this new take.
Might seem like a very strange choice at first but i think he fits in with the current style. As we all know Morbius is Micheal's failed attempted to cure his blood disease. He could quite easily be integrated into Oscorp as a scientist much like Connors. The only thing they would have to do imo is stay clear of the Vampire side. Keep Morbius's design (gotta love that design above he looks pretty bat-like there) but rather than make him drink blood exchange it in for eating people or something along those lines as having a Vampire in a Spider-man movie probably wouldn't look right but a man with Bat-like qualities? That I could see.
Of course an old guy in a suit couldn't work well as a villain in the new franchise but how about the new Vulture? I'm pretty sure they could adapt Vulture to this franchise well by basing him off the new insane, murdering, cannibalistic version that has appeared more recently. The problem here would be finding a happy medium between tech and biology. That would be pretty hard to pull off.
You could quite easily have her as a thief hired by a rival company of Oscorp who wants her to steal their tech and design's (perhaps even that equation Peter gave to Connors?). Alternatively you could go the same route as the other villains and have her as another bi-product of Oscorp's experimentation. I would not normally consider her as a character that should appear but Sony telling Beenox they couldn't use her in the games because they had plans makes me think it could happen. Problem is she's not exactly a villain so they may have to use her as a secondary villain. One reason I would like to see her is because of Garfield's interpretation of Peter. He gave Spider-man the exact amount of nervousness around women to make Black Cat's advances very funny to watch.
I can almost hear people cocking rifles for even suggesting this but it could work. I'm not saying they go down the same route as the Clone Saga but Miles Warren does have all the qualities needed to be a good villain in this series. Gifted scientist, animalistic physicality and he's mad as a hatter. Having him as Oscorp's head scientist could probably work out quite well. I'm not sure how you could turn him from Miles Warren into the Jackal but if accomplished I think he could be a very good villain.
Honorable mentions: These are all characters i'd really like to see but I don't think can be successfully integrated into the new franchise.
Electro, Shocker, Kraven, Mysterio