Well I was thinking about acoustic songs played on the tours, that's why One (you mean the one from Bono solo CD where Michael Stipe is singing? Agree, great version - I only wish it was Bono singing) or Halleluiah here she comes or Stuck didn't make it.
There's a version Bono did with Daniel Lanois and an orchestra the last night of 1999 (for "America's Millennium Gala," whatever that was), in front of the Lincoln Memorial in Washington, D.C. It begins with an odd dedication to Bill Clinton and ends with some lines from George Harrison's "My Sweet Lord" and a bunch of hallelujahs.
Somebody look around on Sicy's FTP for it. If it's not there, I can upload it later.
There's an article here with pictures and a transcript of Bono's introduction.
It's always interesting to hear the song without the Edge. The Automatic Baby version fills the void by adding a little countermelody with Mike Mills' backing vocals, the War Child gives it full orchestral embellishments, and this version throws in a swirling Hammond organ or something, an orchestra to replace the missing synth, and the hallelujahs (assisted by a choir?) at the end, all anchored by some acoustic strumming. Quite nice.
It could have been the night or the time that it happened but Please with Bono and Edge was touching...kind of them sitting in a room and playing it for the first time........