onodrim

To elaborate on an answer already given - The lyrics are from a poem sung by Pippin in the first book, Fellowship of the Ring. The song in its entirety is about three verses long and written by Bilbo to talk about adventure in general. In the book it's quite light hearted; the hobbits are traveling together and having a good laugh. (Chapter III - Three is Company, Fellowhsip of the Ring, for those who are interested. )
I agree that what they did with the lines of the poem in the movie is one of the greatest moments of the film, truly moving. So good in fact that I made it my signature. It's amazing how words can change when you alter the setting in which they're said.

I too was crying from the beacons on.

The reason Frodo was smiling at the end was because he was finally at peace. It wasn't that he was happy to leave his friends or anything like that, afterall he was in essence dying. It was used to show that now Frodo can finally rest. The burden and pain that the ring and war have caused him is over, his whole being just really lightens, and it's a beautiful moment in my opinion. But of course, you have every right to disgree.

Totally understand. If you want something more, there's always The Simirillian and The Untold Tales, and The History of Middle Earth, etc. etc.....one day I'll get to those

__________________
"The world is so exquisite with so much love and moral depth, that there is no reason to deceive ourselves with pretty stories for which there’s little good evidence. Far better it seems to me, in our vulnerability, is to look death in the eye and to be grateful every day for the brief but magnificent opportunity that life provides"
-Carl Sagan