Rav Ovadia and the Dove
A white dove entered the Beit Midrash of Rav Ovadia at 10:00 AM on Erev Rosh Hashana, and landed on Rav Ovadia's Shtender. People tried chasing it away unsuccessfully. Eventually, one learner in the Beit Midrash took the dove and let it go out the window. To everyone's amazement, the dove returned to the same place it was originally - to Rav Ovadia's Shtender, as if it were waiting for him alone. This even happened again - someone took it out, and the dove returned to that exact same spot. It was there until a few minutes before Minha, when Rav Ovadia came to the Beit Midrash, and went to his place. He gently and very mercifully held the dove, caressed it, looked straight at it, and said the following words:
יונה מה תהגי ומה תהמי. נדרך שלמי יען כי אני ה'. וישלח את היונה ולא יספה שוב אליו עוד. עשית שליחותך לכי לשלום אמן כן יהי רצון
With that, the dove flew out the window, and never returned.
The words said to the dove come from an ancient poem of R' Yehuda Halevi and from Parshat No'ah.
Rav Ovadia explained afterwards that these types of occurrances deal with the Neshamot of Tzadikim, who go down to our world to give us a message.
Hashem1.net adds some interesting information by telling us that the Zohar relates a story involving R' Shimon Bar Yohai where he too receives a message from a dove.
He also mentions that the sending away of the dove by No'ah was also done close to Rosh Hashana.