Sam, She is older than me. She is older than I. They are both correct. "Than" has been used as both a preposition "than me" and a conjunction "than I" for the last 500 years Examples from Shakespeare: -I thank God I am as honest as any man living that is an old man and no honester THAN I. William Shakespeare - "Much Ado about Nothing", Act 3 scene 1 -A man no mightier THAN THYSELF OR ME. In personal action, yet prodigious grown And fearful, as these strange eruptions are. —"Julius Caesar" 1600 by William Shakespeare. Examples from modern authors: -Our consul general here is a Columbus man named Streeper, about two years younger THAN ME. —James Thurber, letter, 1 June 1954 . . . someone else who can take it less seriously THAN I. —Robert Frost, letter, 2 Feb. 1920 You have the same choice that Shakespeare had...you can use one or the other and still be correct.

She is older than me. This sentences is correct. She is older than I am. This sentence is correct as well. However, saying only "I" is incorrect. "I" is a pronoun, and is to be used as the subject of a verb. Which is why the second example of a correct sentence that I typed is correct, and the reason why the second sentence you typed is incorrect.

http://grammar.quickanddirtytips.com/than-I-versus-than-me.aspx

Truth is, both.

She is older than me. "than" is a preposition and must be followed by "me" or a complete clause, "I am". She is older than I am.