I think when the average nondancer hears the word "ballerina" they think of a short, petite girl. However, in the ballet world, a dancer shorter than 5'4" will have an awfully hard time finding a corp de ballet job. If he/she is exceptionally talented, a soloist or principal job may be possible. BUt how can you improve without the corp experience...
Personally, I favor small dancers, being one myself. Taller dancers can sometimes look awkward dancing in certain roles. ( I think someone used the Giselle example in a previous reply.) Taller dancers (girls at least) seem to have more trouble with the tricky petite allegro roles that require a lot of quick, short jumping. I guess this might be due to the length of their bodies. Tall dancers do have some advantages though, don't get me wrong. Anything adagio always looks better on a tall, leggy girl to me for some reason.
Height shouldn't matter, rather the quality of the dancing. Unfortunately it does. And america is only getting taller...