And the ending should be played as loud as possible. Seriously, Amarok is my favorite Mike Oldfield piece and I always crank it up.
Also, a fairly obscure New York band called “The Ordinaires” do a kickass instrumental version of Led Zeppelin’s “Kashmir” which also fades out and then back in again.
“Her Majesty” is a funny story. It was supposed to be sandwiched between “Mean Mr. Mustard” and “Polythene Pam,” but the band decided to cut it. It was placed at the end of the tape to be cut, but someone forgot to do it. Oops.
Another Beatles example is “A Day in the Life” which ends with on note that only dogs can hear held for about 30 seconds before the weird endless ending featuring the guys singing the first thing that came to their heads.
Metallica’s “Sad But True” (track #2 on the black album) made me think it was ending about five times the first time I heard it.
“Patience” by Guns ‘n’ Roses is another one. I always think it’s going to end after the whistling part (not at the beginning, the whistling later on in the song.).
Good news and bad news:
Bad News: for years, I didn’t know that there was a spoken pre-song and a coda to “Nights in White Satin”: now I curse whenever it gets cut off on the radio.
Good News: I always thought that one note in aDitL was the best ending (well, one note ending at least) to a song ever. I’m glad now that I’ve never heard the “real” version.
The studio version of “Spoonful” by Cream. The first time I heard Jack Bruce come screaming back in after the long, slow fade–Everything’s a-dyin’ about it!–it scared the hell out of me.
The Roots song, “Step Into the Realm” has this weird beat/background music that keeps fading out. The song always sounds like it’s about to end, especially when the rapped verses end with the music. It’s really kind of creepy.
Quoth umop ap!sdn:
It’s better than that, even… The last line of the song is “It might be just beginning / It might be near the end”. And then the opening bars start up again, as if the song is just beginning.
Oh… I forgot Monty Python’s song, “I’m So Worried.” It has several different false endings!
After fretting about all sorts of things, Terry Jones adds…
"I’m so worried about this very next verse,
It isn’t the best that I’ve got.
And I’m so worried about whether I should go on
Or whether I shouldn’t just stop.
(You think he’s finished, but then he returns with…)
I’m so worried about whether I ought to have stopped.
And I’m so worried because it’s the sort of thing I ought to know.
And I’m so worried about the baggage retrieval
System they’ve got at Heathrow.
(Finished now, right? Wrong! He comes back with…)
I’m so worried about whether I should have stopped then,
I’m so worried that I’m driving everyone round the bend.
And I’m so worried about the baggage retrieval
System they’ve got at Heathrow."
Well, my favorite was in about 1978 or so - my sister bought the 8 track of Pieces of Eight by Styx - I don’t know if anyone else remembers this - but on the song Renegade was at a point where it would switch tracks - there were 4 sections - hell, if you don’t know how an 8-track works, I can’t do it 
Either way it was about the "law man has put an end to my run and I don’t have very long… YEAH!!! looooooonggggg pause while 8 track switches sections** “A renegade, you had it made, etc” Sheesh! What a crummy point to put a break!
“In the Middle of the Night” by Billy Joel has about three of these.
my new favorite singer, Damien Rice does this on the last song of his cd ‘O’. Song is ‘Eskimo’.
He seems to end the song after 5 minutes, then there is silence for 2 minutes.
He does another verse or so for 4 minutes or so and then ends it.
Then there’s silence for another 45 seconds and then the female singer who helps out on here does a 2 minute ‘song’ with anti-war sentiment sung to the sound of ‘Silent Night’. The whole track lasts 13 minutes. It all works well.
Hey neat! I hadn’t thought of it that way. Minor nitpick: the words are “I might be…” but that’s a nice effect nonetheless. Sort of like the aforementioned Nights In White Satin which ends with a spoken piece and a gong sound. It’s the last track on Days of Future Passed, and the first track begins with a reverse gong sound and a spoken part. Enigma’s MCMXCAD also ends the same way it begins.
River of Dreams. It’s a really nice song - I have the album on CD and there’s lots of good music on there.
Paging Mr Blue Sky. 
Just when it reaches what you’re sure must be the finishing cresendo, it starts up again.
“I’ve Seen All Good People” by Yes is virtually two separate songs (Your Move/My Turn) that happen to always be played together. That’s how I took it the first time I heard it on radio.
Iggy Pop seems to have a thing for almost ending a song then going back to the first verse. He does this in T.V. Eye and Sick Of You.
Also Marquee Moon by Television has a pause then starts up again.
Let me in From Eddie Money has a part near the end where everything stops for a couple of seconds, then starts back up again and fades out.
In the music video however, the song stops after the fake ending.
Yes, and I love the sound effect of rustling paper that accompanies the second come-back, like the orchestra members are all checking their sheet music.
That was, I believe, Macca’s idea. For those not old enough to have listened to Pepper on vinyl, there was a time when phonograph arms didn’t have automatic return. If someone didn’t get up to change the record, the needle would stay in the last, “inner” or “playout” groove, indefinitely. One night Macca and some non-Beatle friends were hanging out, smoking up, and started digging the “chig-unk…chig-unk…chig-unk” sound of the needle on the endlessly spinning disk. “Wouldn’t it be cool if there was something in that groove?”
And if you really want to pick nits, I’m not sure that was even the guys singing; I think it was just party noise.