Because it seems no one has taken the time to reply, I guess I will.
Technically, Conan hasn't "revealed his identity yet. He did get pretty close a few times times:
1. M-3: When Kaito Kid finds out Conan is Shinichi. This is non-canon, and Kaito still has yet to prove he knows the two are the same in any canon work.
2. M-6: When Conan gets into the cocoon, Hiroki (as Noah's Ark) realizes Conan is actually Shinichi through some unknown identification program in the cocoon itself. However, he never tells Conan he figured out the secret, and only whispers, "Goodbye, Kudo Shinichi" just before committing "computer suicide".
3. M-10: When the criminal (won't reveal name in case some people haven't watched it yet) uses the fingerprint detectors, he mistakenly takes Conan as Shinichi. Fortunately for Conan, he's also blind and with the help of the voice changing bow tie, Conan can keep his identity a secret.
4. M-13: The most famous, when Irish figures out Conan is Shinichi through a fingerprint matching software. He's killed before he can tell anyone else of his findings, ensuring Conan's secret is still a secret.
If you're looking for the time Conan almost told Ran who he really was, that would be the scene in M-3 where Conan takes off his glasses as prepares to admit, but Kaito Kid interferes.