From the comments at that video link:
"The dude abides... I don't know about you, but I take comfort in that. It's good knowing he's out there. The dude, taking her easy for all us sinners. I sure hope he makes the finals.
Well, that about does her. Wraps her all up. Things seem to have worked out pretty good for the Dude and Walter. And it was a pretty good story, don't you think? Made me laugh to beat the band... parts anyway. I didn't like seeing Donny go. But then I happen to know there's a little Lebowski on the way. I guess that's the way the whole darn human comedy keeps... perpetuating itself, down through the generations.
Westward the wagons, across the sands of time until we... oh, look at me. I'm rambling again.
Well, I hope you folks enjoyed yourselves. Catch you later on down the trail. Say, friend, you got any more of that good sarsaparilla?"
I have no idea why, but I've never felt so touched by any speech from a movie ever.