I always thought - and was taught that the verb 'to be' takes a complement and not an object so that the gramatically correct answer is I, not me. Hence, in the Jackdaw of Rheims, the line: 'Heedless of grammar, they all cried 'That's him!'.' It does sound excessively pedantic now though and I must say I would simply answer the question by saying 'I am.'