Pride (In the Name of Love): Written by U2. Produced and engineered by Brian Eno and Daniel Lanois. Additional engineering: Kevin Killen.
New Year's Day: Written by U2. Produced by Steve Lillywhite.  Engineered by Paul Thomas.
With or Without You: Written by U2. Produced by Daniel Lanois and Brian Eno.  Engineered by Flood. Mixed by Steve Lillywhite.
I Still Haven't Found What I'm Looking For: Written by U2. Produced by Daniel Lanois and Brian Eno.  Engineered by Flood. Mixed by Daniel Lanois.
Sunday Bloody Sunday: Written by U2. Produced by Steve Lillywhite. Engineered by Paul Thomas.
Bad: Written by U2. Produced and engineered by Brian Eno and Daniel Lanos. Additional engineering by Kevin Killen.
Where the Streets Have No Name: Written by U2. Produced by Daniel Lanois and Brian Eno. Recorded by Flood with Pat McCarthy.  Mixed by Steve Lillywhite.
I Will Follow: Written by U2. Produced by Steve Lillywhite. Engineered by Paul Thomas.
The Unforgettable Fire: Written by U2. Produced and engineered by Brian Eno and Daniel Lanois.  Additional engineering by Kevin Killen.
Sweetest Thing (The Single Mix): Written by U2. Produced by Steve Lillywhite and Daniel Lanois and Brian Eno.  Recorded by Joe O'Herlihy and Pat McCarthy.  Additional recording and mixing by Steve Harris.  String arrangement by Daragh O'Toole. Strings: Una O'Kane, Nicola Cleary, Aengus O'Connor, Nicholas Milne.  Special Thanks to Ali Baba.
Desire: Written by U2. Produced by Jimmy Iovine.  Recorded by Paul Barrett. Mixed by Shelly Yakus and Rob Jacobs.
When Love Comes to Town: Written by U2. Produced by Jimmy Iovine.  Vocals and guitar by B.B. King.  Percussion by Ms. Bobbye Hall.  Backing Vocals by Rebecca Evans Russell, Phyllis Duncan, Helen Duncan. Recorded by Dave Ferguson and Cowboy Jack Clement. Remixed by Shelly Yakus and Rob Jacobs. 
Angel of Harlem: Written by U2. Produced by Jimmy Iovine. Recorded by Dave Ferguson and Cowboy Jack Clement. Mixed by Rob Jacobs and Shelly Yakus. Organs by Joey Miskulin.  Horns by the Memphis Horns.
All I Want is You: Written by U2. Produced by Jimmy Iovine.  Recorded and mixed by David Tickle.  String arrangement by Van Dyke Parks.

Due to elevated prices on domestic CDs, and the fact that it is often cheaper to buy imports, an additional bonus track was added in Japan to make the domestic version more attractive.  For this compilation, the bonus track is "One Tree Hill".  The bonus track was also included in the vinyl release.

Several differences have been noted between the tracks on this compilation and the various versions that had been released prior.  If there isn't a mix name listed above the version is the same as the album version.  Below are some notes on the differences between tracks:

Bad: This is an edit of the version found on The Unforgettable Fire. This version drops several "Whooo hooo hoos" found in the original version.
Where the Streets Have No Name: This is an edit of the 5:37 version found on the Joshua Tree album. This is not the same as the version found on the single which is 4:46 in length and features additional backing vocals by the Edge.
When Love Comes to Town: This version of the song features an extra guitar lick you can hear at about 4:12 in the Best Of version.  This takes the total time of the track on this release to 4:17 from 4:15 which it was on Rattle and Hum.

October was actually a hidden track at the end of the album.  After All I Want is You ends, there is a period of blank space and then October starts as part of the same track. October is not listed on the back tracklist of the CD.