Prescriptive grammar requires objective pronouns to follow prepositions. Since between is a preposition, standard written English uses the objective me rather than the subjective I. Too many people like to argue that between you and I is common in regular usage and should therefore be considered acceptable. This argument (common in grammatically-lax circles) depends on unprovable anecdotal exposure; written evidence shows that all English writing overwhelmingly prefers the standard and correct form, between you and me.