I just rewatched Tapestry this afternoon, and while it isn't really a full-on speech, the emotional depth & real meaning Patrick Stewart puts into these scenes is superb. The fact that the message is so true anyway only adds to the depth:
I think I like his final conversation with Riker even more as it reveals that he really has changed, and come to terms with his own identity, but I couldn't find that online. A transcript will have to do:
PICARD: I still don't know what to make of it. Was it a dream? Was it one of Q's elaborate tricks?
RIKER: A lot of people near death have talked about strange experiences, but I've never heard one so detailed.
PICARD: And, you know, there's still a part of me that cannot accept that Q would give me a second chance, or that he would demonstrate so much compassion. And if it was Q, I owe him a debt of gratitude.
RIKER: In what sense? It sounds like he put you through hell.
PICARD: There are many parts of my youth that I'm not proud of. There were loose threads, untidy parts of me that I would like to remove. But when I pulled on one of those threads it unraveled the tapestry of my life.
RIKER: I was just trying to imagine a hell-bent for leather young officer insulting a Nausicaan twice his size. I wish I'd had a chance to know that Jean-Luc Picard.
PICARD: Oh, well, to tell the truth, that wasn't the first run-in I'd had with a couple of surly Nausicaans.
PICARD: Oh, yes. During my sophomore year, I was assigned to training on Morikin Seven. Well, there was a Nausicaan outpost on one of the outlying asteroids, and one day...