Actually, Kennedy said the phrase two times. The first time, he made the analogy to Rome: “Two thousand years ago ... (repeating because of the noise) two thousand years ago, the proudet boast was: civis romanus sum. Today in the world of freedom, the proudest boast is ´Ich bin ein Berliner´” and as he finishes his speech he said it again in the context of “all free men”.
I still say he said, “Ik bin ein Berliner.” ;)