Ran's birthday is usually seen as something important in the anime and manga and is talked about a lot. Yet, throughout the entire series of 660+ episodes and 70+ volumes, it has never actually happened.
Why is Ran's birthday so important to the plot?
Officially, neither the birthday is revealed, nor has it really played a role in the plot.
However, Aoyama said in an interview, that there is an "obstacle" preventing him from revealing Ran's birth date, but since the birthday hasn't passed Ran is 16 right now"
The interview, quoted from Detective Conan World's forum:
蘭の誕生日教えて！→差し支えあるので今は言えない。でもまだ誕生日来ていないので蘭は現在16歳。
Tell me about Ran's birthday! → Since there's an obstacle, I can't tell it for now. But since the birthday hasn't passed, Ran is 16 right now.
I think that a future volume will be about her birthday, so everything else would be wild speculation.
