1 - Until the End of the World (1991, Achtung Baby) (performance from Boston 2001)
This is my favorite U2 song overall, also. It sums up perfectly what I love about U2: Biblical imagery, great guitar solos, a steady determined beat and bass line, and enough emotion, Spirit, and rock to get everyone's attention. The song has been done differently on every tour, but it has yet to feel tired. Adam Clayton has even remarked that it is one of his favorite songs to play live because there is just so much you can do within it. Also, my first U2 concert, Chicago back in 2005, they played this song for the first time on the tour...and I think you can hear me scream on the bootleg.
2 - The Fly (1991, Achtung Baby) (performance from Sau Paulo, 2006)
Another great live Achtung Baby song, of which most of my favorite songs are from. I tend to like U2's rockers live more than the acoustic stuff. This song has some great poetic lines and comes from a very literary place in Bono's psyche. Also contains one of Edge's best guitar solos ever. If someone ever tells me that U2 doesn't know how to rock, I always direct them to this sensory overload of a song.
"Every artist is a cannibal, every poet is a thief/All kill for inspiration, and then sing about the grief." This fits in perfectly with CS Lewis' Screwtape Letters, one of my favorite books.
3 - God Part II (1989, Rattle and Hum) (performance Australia, 1989)
Only performed on one tour, the Lovetown tour, this song is a lost rocker that needs to come back. A sequel to John Lennon's "God", the song takes those ideas and spins it on its head while rocking the house. There are only a few really great performances available of this song to choose from, but all of them are excellent. If I ever had to request a song they haven't played in a long time, it would be this song...probably.
4 - Last Night On Earth (1997, Pop) (performance Mexico City, 1998)
Another song that was only around for one tour (so far). A lead-in for Until the End of the World, it's a great riff mixed with some pretty cool visuals, although the cartoon part can get annoying. However, the garage band rocking out that happens at the end is excellent...you can tell the band is just having fun, who cares what anyone else thinks.
5 - Where the Streets Have No Name (1987, Joshua Tree) (performance Slane Castle, 2001)
This is the test of a U2 fan: when the lights turn red during the organ, and the band starts playing...the moment the stadium is awash in white light, if you don't feel a chill down your back, you aren't a U2 fan. This has been the standard test for decades. Yes, it's not my favorite live U2 song, but it's arguably the most important. Biblical imagery, written mainly while Bono was in African in '86 with his wife, coupled with the most often stolen riff from the Edge, makes this the one song that can turn any bad U2 performance completely around and allow the Spirit of God to descend.
Bonus songs - 11 O'Clock Tick Tock (various live performances, this song can be up or down); A Sort of Homecoming (only from Wide Awake); Discotheque (gets better each reworking); Please (Rotterdam 97); Love and Peace or Else; Running to Stand Still (ZooTV with the hallelujahs); All I Want Is You.