grammaticality - Older than me (or I)?

Is it correct to say, "She's older than me" or "She's older than I?" I almost always hear people say the former (me). If I remember correctly my grade school grammar, though, the test to apply is to say the sentence out in full: "She's older than I (am old)." In that case, the subject form I seems to be correct.

I've often wondered and would appreciate a definitive answer.