I realize that this is going to be a select group - most bands, even those with extensive discographies, have never even recorded a song which would fall into this category. Heck, the Beatles I don't think ever even cracked the TEN minute barrier, and the Stones only once. Nevertheless, I thought I'd list some of my favorites of this type. A song over fifteen minutes long, should justify its length in my opinion, in other words not be just the same guitar lick repeated over and over ad nasuem.
I'm only considering studio versions of songs here, not live expanded versions of a studio song less than a quarter-hour long. However, songs with differently tracked "parts" can be put together and their running time derived from the total.
Anyway, here's my list, ranked by running time.

43:45 "Thick as a Brick", Jethro Tull
35:37 "Remember The Future", Nektar
23:28 "Echoes", Pink Floyd
22:51 "Supper's Ready", Genesis
22:43 "Nine Feet Underground", Caravan
22:05 "Lizard", King Crimson
21:49 "The Gates of Delerium", Yes
21:14 "Birdman", McDonald and Giles
20:39 "Tarkus", Emerson Lake and Palmer
20:32 "2112", Rush
19:57 "The Fountain of Lamneth", Rush
18:39 "Close to the Edge", Yes
17:07 "Inna Gadda Da Vida", Iron Butterfly
16:42 "A Tab in the Ocean", Nektar
16:13 "Salisbury", Uriah Heep

I left obvious choices like Procol Harum's "In Held Twas in I" and ELP's "Karn Evil 9" because I felt that although each song has their moments, they also have a lot of boring passages as well.

BTW, "Thick as a Brick" may just be the longest song in rock history, if there is one longer, I don't know of it.

Well as a Marillion fan, I'm bound to nominate Grendel, at around 17 minutes. A wonderful piece of mythology/horror based on the Beowulf saga, with a twist at the end when we hear Grendel's point of view:
Why should I feel pity when you kill your own and feel no shame?

Also, from a completely different phase of Marillion's career, This Strange Engine is also magnificent and moving piece, journeying through various styles as we journey through a child's life, homely, poignant and shocking.

(This Strange Engine scrapes in at around 15:30)

Chicago Transit Authority comes close with it's 14:39 song titled Liberation (AND only 3 words of lyric in the entire song!) ...

Since, I'm too lazy to dig through my collection - and can't, off hand, think of any songs that aren't jazz or classical music compositions - I'm going to cheat. From The Book of Rock Lists by Dave Marsh and Kevin Stein:

"By the Time I Get to Phoenix" - Isaac Hayes (18:40)

"Alice's Restaurant Massacre" - Arlo Guthrie (18:30) (Guthrie created a vitual cottage industry with "Alice". Or so it seems.)

"In Held 'Twas I Suite" - Procol Harum (17:51)

"Sister Ray" - Lou Reed

np - "Disppointed" - Public Image Limited

"It's all one song." - Neil Young

Um, waitaminute. You asked for best songs over 15 minutes. Okay. I don't know of any rock songs that last that long and are that good.

If genre is no object, then

"Zimbabwe" - Miles Davis (41:18)

"Gondwana" - Miles Davis (46:50)

(Both from the album, Pangaea.)

And

"Right Off" - Miles Davis (26:52)

"Yesternow" - Miles Davis (25:34)

(Both from A Tribute to Jack Johnson.)

np - Couldn't Stand the Weather - Stevie Ray Vaughan and Double Trouble

"It's all one song." - Neil Young

Oh, and ignore my previous list. I really have never heard any of those songs on it. No. I take that back. I do know "Sister Ray" by the Velvets. Not a bad song.

"It's all one song." - Neil Young

"In the Garden of Eden" by I. Ron Butterfly

Gee, are we alowed to mention that one on this board?

Anyway, the CD booklet doesn't list a running time, and I'm too lazy to actually stick the thing in my stereo and find out at the moment, so Ill have to ask you if "Voodoo Chile" by the Jimi Hendrix Experience is long enough to qualify (Not "slight return", mind you. I'm talking about the long version on Electric Ladyland)

np - Thirteen Tales From Urban Bohemia - The Dandy Warhols

Yeah, "Voodoo Chile" qualifies. According to http://www.allmusic.com/cg/amg.dll?p=amg&uid=MISS70306161910&sql=At69ks39ba3bg it's 15:05 long.

np - "Dr. Feelgood" - Aretha Franklin

"It's all the same song." - Neil Young

>Well as a Marillion fan, I'm bound to nominate >Grendel, at around 17 minutes.

Oh yeah, Marillion's a great band. I don't think I've heard "Grendel" though.

I have it on an EP. Side 1 is Market Square Heroes and Three Boats Down From The Candy, side 2 is Grendel. Fish era, of course.

At Amazon I found it in these products:
The Collection
B'Sides Themselves
The CD Singles Vol.1 1982-1988 [SINGLE] [BOX SET]

Oohh! Ooh! I've thought of another one. A personal favorite of mine -

"Carnage Visors" - the Cure (27:00)

np - War - U2

"It's all one song." - Neil Young

The Live Killers version of "Brighton Rock."

Here's another one that I'm not really sure about: Ten Years After's performance of "I'm Going Home" Clocks in a little under 10 minutes long on the soundtrack album, but the whole performance, as seen in the film, is a lot longer. Unfortunately, I can't get a definate time for that, so I'm not sure if it qualifies or not.

np - Electric Sweat - The Mooney Suzuki

I am probably the only one here who thought of mentioning this:
"Achilles, Agony and Ecstasy in Eight Parts" by Manowar (28:38)

"State of Independence" by Moodswings (15:52). It was used over the closing credits of Single White Female.

I was going to post the Finale to Beethoven's 9th Symphony (Ode to Joy), but realized this is for rock... (It isn't in the board title)

I LOVE Ode to Joy! (That and Mozart's Overture to the Magic Flute are the two classical pieces that I really like.) However, the version of Ode that I have is only 12min, 38 sec. long.

But who says this board is for rock?

"This Corrosion"-- Sisters of Mercy

I remember driving from one end of town to another hearing ONLY this song on the radio.

Well, since I can't post any Blue Öyster Cult songs without resorting to live versions... I'll have to list songs by "The Master", my second favorite artist - Mr. Miles Dewey Davis III, aka The Prince of Darkness. Well, considering that I hardly ever list anything by Miles, I guess now's as good a time as any to make up for it somewhat.

"Helen Butte" (16:07)
"Shhh/Peaceful" (17:58)
"In a Silent Way/It's About That Time" (19:57)
"Concierto De Aranjuez (Adagio)" (16:19)
"Pharaoh's Dance" (20:05)
"Bitches Brew" (26:58)
"Spanish Key" (17:32)
"Lonely FIre" (21:09)
"Guinnevere" (21:07)
"Recollections" (18:54)

np - Kiss of Life - Gene Loves Jezebel

"It's all one song." - Neil Young (Just that some tunes are longer than others.)

Sophie's post of 7/6 convinced me this week to go out and purchase Marillion's Script For a Jester's Tear, an album I hadn't really listened to in about 15 years. I've got it on now.

The Pink Floyd instrumentals

Sophie, I gotta say I prefer TSE to Grendel...but I'm more of an H-era fan. This does not stop "Clutching at Straws" from being my favorite Marillion record, however.

"Tubular Bells", by Mike Oldfield, runs about 45 minutes. It may equal or just beat "Thick As A Brick" in running time. (I don't have a copy available right now, and CD Now.com doesn't list running times.) Most people recognize the opening riff, as it was used in The Exorcist. Ironically, Mr. Oldfield just released a brand new recording of this, "Tubular Bells 2003," using the latest technology.