I respectfully disagree with Dyturtle. When Peter first kisses Gwen, he wasn't under the influence of the symbiote just yet. It was a publicity stunt. read more
Peter Parker kissed Gwen Stacy because he was under the influence of Venom. Throughout the whole movie you can tell Peter started to act differently the more he worn the black Spider-Man outfit (Venom). Peter even started to change his hairstyle and wear more black. read more
During the second"Clone Saga", Gwen Stacy's clone, now married to a clone of Professor Warren named Warren Miles, sees a copy of Peter Parker's book of Spider-Man photos, Webs, and remembers (to an extent) her real history. read more