Shine On You Crazy Diamond pt 6-10 is my favorite outro of all-time (although one could argue its “Power”)
Doors - Touch Me
Beatles - Strawberry Fields
Starship Trooper from The Yes Album. Most awsome guitar solo ever!
Go 'SC! Beat the Wolverines!
Ah, now I perceive why NoCoolUserName didn’t need to put any effort in username selection.
I really like how Led Zeppelin’s “Ramble On” degenerates into chaos, and if you’re going to nominate “Layla”, then you should also throw in a nomination for “White Room”.
IIRC, the last song on Pearl Jam’s Ten looped back into the first song, making the whole album its own intro/outro.
I don’t have her albums onhand, but I know Tori Amos has done the massive explosive outro you’re envisioning, as well as the quieter, all-piano outro similar to Phish’s live cut of “Squirming Coil”. Their “Run Like An Antelope” is also stunning.
David Bowie, “Space Oddity”.
The Who, “Won’t Get Fooled Again”.
Two by Guns n’ Roses, the first is Rocket Queen when the song transforms from a cocky, in your face attitude to a heartfelt, emotional plea of love. The second song is Coma, Slash’s guitar emulates the tone of a heart rate machine as it flatlines, an awesome song that always sends chills down my spine.
Finally, the ending to Courdoroy by Pearl Jam. The mood it envokes is one of powerful melancholy as ones deepest feelings are realized.
Again displaying how old I am:
Pilgrims Progress by Procol Harum. Amazing drumming and percussion, added layer by layer.
Accidents by Thunderclap Newman. What can I say? You’ve just gotta hear this! (“Life’s just a game/you fly a paper plane/there is no end”)
Peter Green’s blistering solo on the outro to Black Magic Woman (yes, the original 1969 Fleetwood Mac version).
I always liked the way Heartbreaker went right into Living Loving Maid on Zep II. The radio stations just said the hell with it, it’s all one song. 
The Beatles Carry that Weight. The second time the chorus starts (Boy, you’re gonna carry that weight, carry that weight a long time…) I always feel the need to crank up the volume.
Also the end of Get Back. That’s the main problem I have with Let it Be Naked. The ending line is missing.
Jimi Hendrix Experience
“Bold As Love”
Not only some of my favourite outros but also on my favourite final tracks on of some of my favourite albums.
In no particular order
1 Lonely Planet - Last track on the album Dusk by The The
2 Street Spirit - Last track on the album The Bends by Radiohead
3 I Am The Resurrection - Last track on the album The Stone Roses by The Stone Roses
4 You Can’t Always Get What You Want - Last track on the album Let It Bleed by The Rolling Stones
5 Anywhere I lay my head - Last Track on the album Raindogs by Tom Waits
6 Still Life - Last track on the album Dog Man Star by Suede
7 Lord Can You Hear Me - Last track on the album Let It Come Down by Spiritualised
8 We Float - Last track on the album Stories From The City, Stories From The Sea by PJ Harvey
9 All Apologies - Last track on the album In Utero by Nirvana
10 Why D,Ya Do It - Last track on the album Broken English by Marianne Faithful
The first thing that popped into my head was the end of Epic by Faith No More. The end of the Source Tags And Codes title track by Trail Of Dead is also beautiful.
The Dream’s Dream outro by Television has a delicious “eerieness” about it.
“Stronger Than Dirt.”
Blotto - Metalhead is the best outro in rock music, ever, IMO. It’s a great song, but that ending just kicks all kinds of ass. 
ETA: BTW, that’s Buck Dharma playing the guitar solo!
The ending of Genesis’ “The Musical Box” always gives me chills.
She’s not There by The Zombies? I guess that doesn’t really have an outro.
A while ago I made a thread about the best fade out guitar solos in songs. I think the top two are from Steely Dan. Kid Charlemagne (Larry Carlton on guitar) and My Old School (Skunk Baxter on guitar).
ETA: My old thread.
Megadeth: Five Magics. Pure, metal reckless abandon.
-Prince and the guitar solo at the end of “Let’s Go Crazy”.
-The epic drum fill at the very end of Judas Priest’s “Sinner”.
-Dire Straits “Down to the Waterline” with the last run of guitar over a nice drum fill.
-AC/DC “Kissin’ Dynamite” with that fall-apart drum solo. I don’t recall ever hearing any other song that ended like that.
ELO’s “Mister Blue Sky” has a nice outro that didn’t get played much on the radio. In addition, it’s the outro for that entire side of that LP–“Concerto For A Rainy Day,” from, “Out of the Blue.”
Yes sir. Yes, indeed.
At any rate my nomination is “Long Red”, by Mountain on their "Mountain Live: The Road Goes Ever On" album. I’ve got a few more in my brain, but, I can only recall this one, right now.