Don’t Cry For Me Argentina
Have I said too much? There is nothing more I can think of to say to you.
But all you have to do is look at me to know that every word is true.
Does the piano coda in “Layla” count?
If not, “You Can’t Always Get What You Want”.
Amazing image! And I know precisely what you mean about it. Cool! 
The Fez, by Steely Dan. Ends with a guitar solo that progressively gets more “Arabic” sounding as the song fades out.
*Criminal * by Fiona Apple. Similarly, ends with about a minute and a half of creepy layered instrumentals, with the reed-organ and flute sounds playing scattered melodies (including “The Snake Charmer”) over the song’s great rolling drumbeat.
Pink Floyd -The great Gig in the Sky - Clare Torry vocals
And then there’s I Want You (She’s So Heavy), which has that shocking, arresting stop.
I’ve always liked the Beatles better than the Stones, but for me, the ending of You Can’t Always Get What You Want tops the scatting in Hey Jude.
Boz Scaggs’ Loan Me a Dime ends with a great solo from Duane Allman.
The outro on “Bold as Love” closes out not only the song, but the album that I think was Jimi Hendrix’s best. It’s also the first use of flange in rock history.
Sheep as well.
And Shine On part II. And Echos. And…
Tull’s Baker Street Muse.
Absofrickinlutely.
Hey, thanks for mentioning Bill Nelson! I love the way he finishes up “No Trains to Heaven”.
FREEBIRD!!
Well I like it
No, that was on “The Big Hurt” by Miss Toni Fisher, in 1959.
“School’s Out” by Alice Cooper runs slower and slower, then grinds to a halt.
…and Welcome to the Machine (although I sort of dislike the pingpong ballish sound at the very end, they could have replaced it with a different sound.)
“Fade Away” by Sloan, ends with a classic-rock-style outro, which oddly enough does not fade out 
I’d also nominate Sweet Hippie (or is it Go, Hippie?) by Fountains of Wayne, which also has the same style of outro, except that they decided to do this as the last song in their concert when I saw them, thus leading to an anticlimactic finish when the lead singer walked off with just the guitar player rambling for X minutes.
And when Coheed and Cambria pulled the exact same stunt when I saw them, I decided that modern rock bands just don’t know how to end a concert with a classic rock style song. (Although I must say, the last time I saw Heart they opened with a not very appropriate song: Mistral Wind. That’s more of a late in the first set or early in the encore type song, but the first two times they opened with Kick It Out, which while merely a decent song is a good opener.)