The episode where Picard and Wesley are stuck in a cave with no water and Picard passes out from dehydration.
Wesley find the water spring and hand feeds the water to Picard and insists that he live.
After the way Picard treated that kid and Wesley still wanted to save his life...well, I don't know that I would've been as compassionate Wesley.
That episode has a lot of good moments and was a very nice send-off to Wesley. I liked Picard's parting words to him.
I don't think any scene in TNG has made me want to cry, I'm not usually prone to crying at movies/TV. But that's not to say there are not a lot good, emotional, scenes in the series.