11 O'Clock Tick Tock - New York, March 17th 1982: A great extended(6 minutes) version with a great guitar solo and "Give Peace a Chance" snippet
The Electric Co. - East Rutherford, May 15th 1987: I just love when Bono adds some Doors in a song...especially this one.
Sunday Bloody Sunday - Denver November 8th 1987. Definitely the Rattle and Hum version.
The Unforgettable Fire - Glasgow, November 6th 1984
Bad - East Rutherford April 15th 1987 (Amazing 16-minute version)
Where the Streets Have No Name - tie between Dublin, December 26th 1989(probably best Bono's vocal performance) and Sao Paulo, January 31st 1998
I Still Haven't Found What I'm Looking For - Rotterdam, June 11st 1993. This is BY FAR the best version of this song. A semi-acoustic version, beautifully performed, with added lyrics!
With or Without You - Dublin, June 28th 1987. A beautiful 8-minute version with Shine Like Stars, where Bono plays this little beautiful acoustic guitar solo.
Bullet the Blue Sky - New York, August 29th 1992. Rock and roll at its finest.
Running To Stand Still - Rotterdam, January 6th 1990. Fantastic extended version with an amazing outro with new lyrics.
One Tree Hill - Dublin, December 26th 1989. A must listen for every U2 fan.
Exit - Simply an amazing 6-minute performance with some crazy Edge and snippets of Van Morrison's Gloria, Doors' Riders on the Storm and Silver and Gold.
Hawkmoon 269 - Brisbane, October 3rd 1989. This is one of U2's best live songs. Period.
All Along the Watchtower - New Year's Eve 1990.
Desire - Rotterdam, January 10th 1990. U2 goes metal big time with a huge shredding solo by our man The Edge.
All I Want Is You - Dublin, December 30th 1989. As Jick already mentioned, the best version of the song is this. A very cool small Bono guitar solo at the end.
That's for the 80's...