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To quote Wikipedia:

In fact, Kennedy's statement is both grammatically correct[4] and perfectly idiomatic, and cannot be misunderstood in context. The urban legend is not widely known within Germany, where Kennedy's speech is considered a landmark in the country's postwar history.

The citizens of Berlin do refer to themselves as Berliner; what they do not refer to as Berliner are jelly doughnuts. While these are known as "Berliner" in other areas of Germany, they are simply called Pfannkuchen (pancakes) in and around Berlin.[10] Thus the merely theoretical ambiguity went unnoticed by Kennedy's audience, as it did in Germany at large. In sum, "Ich bin ein Berliner" was the appropriate way to express in German what Kennedy meant to say.

You can read the whole article on JFK here: http://en.wikipedia.org/wiki/Ich_bin_ein_Berliner

I'm hungry now.