In The Amazing Spider-Man, why does Peter not get badly affected by the poisonous venom spider, while both Harry and Connors (used lizard serum) do?
This is explained in the second film - Peter's father altered the Spider's DNA with his own, meaning only Peter could have gained the benefits from it. This was the ensurance that after Peter's father's death (which his father expected would happen) the power would stay safe and die with him.
Here is the direct quote from the script:
Richard Parker: It doesn't matter because there is something else that Norman doesn't know. The Human DNA that I implanted in the spiders was my own, which means that without me, without my bloodline, OsCorp can never replicate or continue my experiments.