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The concert that impressed me most, was Radiohead in 1997, Vredenburg, Utrecht, Holland, shortly after the release of OK Computer.
To concerts of Tröckener Kecks (Dutch rock band) I have good and special memories. Saw them a couple of times in Tivoli, Utrecht, Holland.
In 2007 I've seen 17 Hippies here in Freiburg. A 'world music' band from Berlin, was very nice.
Last summer, end of June, I was in Canada for holiday and visiting my mother in law. I really regret that I did not get tickets for Wilco in Toronto, I was in town that day! 
Yes, nicolas, their concerts are boosting the happy hormones big time. Their CDs are also nice to listen to, but the real acclaim they get from their live performances.
So, let's agree upon listening simultaneous to 17 Hippies twice this coming summer: First, when France and Holland play in the group phase of the European soccer championships, and the second time when they meet again in the final. 
yes ! 
but will you still play them after the final ? 
Sure, it would mean Germany won't win the tournament, right?
My favorite was probably Johnny Cash at the State Theatre in Detroit after the American Recordings album came out. This was probably in 1994. Johnny was still very spry and in good voice. Part of the concert was oldies with the small band, part was accoustic numbers from the new record, and part was with June just like the Folsom prison show. It was a review of his whole career and he was really into it.
The runner up would be Bruce Springsteen, July of 1984, during the first leg of the Born In the USA tour at Joe Louis Arena (hockey rink). Long energetic show with great sound and a wild crowd. The next time he came around, in 1985, he played the Silverdome (football stadium) and it was terrible by comparison. My Bruce fandom never recovered...
Third place goes to The Replacements at the Michigan Theatre in 1989 (towards the end of their career as a band). They were still fun, but not complete drunks like earlier shows I'd seen.
Honorable mention: Bob Dylan, Tom Petty, and The Grateful Dead at the Akron Rubber bowl in 1986. More for the scene than for the music. First (and only) Dead show. Highlight was the Dead's version of Desolation Row. (This was followed by a ten-minute drum solo. 
)
Related questions:
(1) What is the biggest act that you saw in the smallest venue (before they were stars)?
I missed a chance to see R.E.M. at my neighborhood college bar in 1984. U2 played there a few years earlier. The next time R.E.M. came around the venue was a bigger theatre. Later, while was living in Ann Arbor in the late 1980's/early 1990's bands like Pearl Jam and Nirvana came through and played the same small bars before getting famous. Other than the Pixies, I never saw any of the bands that made it big, unless you want to count Uncle Tupelo.
(2) Who is the oldest legendary/iconic performer you have ever seen? (I'm not talking about the performer's at the time of the concert, but in terms of who was born first. E.g., Maybe you saw Louis Armstrong when you were a kid, or something like that?)
Other than Johnny Cash, I've seen Frank Sinatra, James Brown, and John Lee Hooker. All four were very entertaining.
This would be a very difficult list to compile! I know the worst, though- I was dragged to a Dave Matthews Band concert by my wife, and it was as scarringly awful as I anticipated it would be. My wife even hated it! I do have some really interesting concert experiences though, including the Madonna DVD appearance that Anthony refuses to admit to adoring. 
With all these great concerts mentioned, I allow myself to mention the worst concert I've ever been to.
Back in 1990, they made one of the best britpop albums to date, but live it was a complete disaster to listen to ... The La's. When artists are stoned and/or drunk, the difference between a studio-recorded CD and a live concert becomes very evident. Shortly after the concert, they broke up... 
Anthony : yes I was. remember he sang a Piaf song, but in fact I'm afraid I don't remember much more. Oh yes : opening was Keb' Mo', a sort of fake bluesman I liked very much (but not so much anymore). Oh yes, I was with my ex-girlfriend, the one who loved JB.
One of my friends came across him in Paris on the boulevard St Michel the day before the concert and chatted with him. He was very friendly.
Loophole : Man, I wish I could... But money and family will keep me from that I'm afraid
And Chicago is a city I'd really like to see, cause you know I'm a blues fan, but not only. All myfriends that went there loved it.
When I was doing my 1980 lists I planned to include, apart from albums and singles, my favourite movie and my favourite live show. But, seeing quite difficult to point a “memorable” live show from every year I’ve decided to make a Top 10 reviving this thread. And, thanks to Internet, I’ve found the exact date of almost every concert. So, ladies and gentlemen,…
1. AL TALL + OVIDI MONTLLOR + LLUÍS LLACH (Bull Ring, Valencia, 3 October 1981)
One of my very first live shows (I was fifteen), and a politically highly-charged one. Apparently not everyone was celebrating the brand new freedom after long years of dictatorship, so some ignorant fascists put a bomb in the house of Joan Fuster, one of the most brilliant intellectuals of my homeland. But they didn’t succeed. They couldn’t shut his/our mouth. I still get chills when I remember Llach singing “Campanades a morts” (“Bells Ringing for the Dead”
and shouting “Assassins!!”.
2. ALASKA Y LOS PEGAMOIDES (Galaxy Disco, Pobla de Vallbona, Spring 1982)
Not many people gathered round the stage in a small village disco to see the icons of the “Movida Madrileña”. But I admit that it shocked me (or at least a young and impressionable me). Expecting to find the new wave colourful look and bright sound of its records I found a band with gothic look and punk energetic sound. This performance pushed me into modernity, into looking forward and not back in pop history. Of course I changed my mind years later but I don’t regret at all embracing fashion and modernity during my teenage years.
3. DEPECHE MODE (Pachá Auditorium, Valencia, 3 March 1984)
A great concert from a quite early incarnation of techno-pop masters (without Clarke but with the glorious line-up of Gahan-Gore-Fletcher-Wilder). No guitars and no drums but nobody missed them. They were about to improve notably in a few years, but then Dave Gahan was a perfect front-man yet and the songs were superb (“Everything Counts”!!). I was playing in a punk-funk band then and I remember that my friend Raúl asked me: “Why don’t you play songs like these ones?”. And I told him: “Believe me, it’s not easy at all. I wish I could”.
4. ECHO & THE BUNNYMEN (Pachá Auditórium, Valencia, 24 May 1984)
God bless Pachá Auditorium. We didn’t have in Valencia a club with medium capacity that allowed concerts of bands not successful enough to fill stadiums but known enough for not playing in a small club. For me it was like a Pop Church where I went religiously during the eighties. I could point many concerts but I’ll point a fantastic one from the second Fab Four from Liverpool. They came to promote an acoustic-based album (“Ocean Rain” but its set was tremendously intense and noisy. The buzzing in my ears lasted for more than two days.
5. BRUCE SPRINGSTEEN & THE E-STREET BAND (Vicente Calderón Stadium, Madrid, 2 August 198
Despite the 40ºC stifling heat and the stadium packed with thousands of people Bruce Springsteen gave us no rest at all, the intensity didn’t decline during more than 4 hours of concert. And I know that you believe me for sure. The ritual of rock ’n’ roll live shows at its maximum expression. Going to see a massive rock star at the height of his popularity is (almost) always a powerful experience, but if we talk about The Boss and his E-Street Band you can multiply the impact by ten. Glory days.
6. PRINCE & THE NEW POWER GENERATION (Luis Casanova Stadium, Valencia, 24 July 1990)
I know, the movie “Graffiti Bridge” was not “Purple Rain”, the album was not “Sign ‘O’ the Times”, the “Nude” Tour was not “Lovesexy” Tour and even The New Power generation were not The Revolution. But a Prince show is always a Prince show. Not simply a rock concert but a complete show, the perfect way to showcase the exceptionality of Prince as musician (what a superb guitar player!), singer, dancer and showman. Sex, music, dance, romance.
7. BOB DYLAN (Luis Puig Velodrome, Valencia, 21 July 1995)
This performance falls into the category “come on, let’s go to see him before he dies” in which I could include The Stones or Lou Reed too, although all of them continue alive and kicking. Part of the “Never Ending” Tour, Dylan completed an awesome concert despite the fact that his latest release was an uninspired “MTV Unplugged” album. Some highlights included the country section (with “Don’t Think Twice It’s Alright” or “I’ll Be Your Baby Tonight” but mainly a wild take on “All Along the Watchtower”. You could actually “see” the electric waves coming from the stage shaking the audience.
8. GORAN BREGOVIC (Cultural Centre, Burjassot, 17 May 2003)
A brothers concert. One of the few occasions in which my brothers and me went to a show together. My brother Jesus (yes, it was quite common in Spain naming Jesus the boys born just before Christmas) was a big fan of Bregovic and the Wedding and Funeral Band and introduced my brother Miguel and me in such wonderful Balkan music, that night more apt for weddings than for funerals. By the way, Jesus is the real genius of my family, a gifted musician and an expert in flamenco and folk music (one of these days I will finally convince him to make a list).
9. RADIOHEAD (Las Ventas Bull Ring, Madrid, 16 July 2003)
No doubt, one of the best live shows I’ve ever seen. With Low as support band, Radiohead made a great concert with a perfect balance between rock and electronica, between intimate and cathartic moments, between avant-garde and accessibility, between classicism and modernity. And moreover my wife Ana insisted in waiting to meet the band outside the Bull Ring. After two hours (the things one can do for love!) Thom Yorke showed up and, surprise surprise, he talked with Ana for a few minutes. He was really gentle and nice considering the late hours.
10. PIXIES + MORRISSEY + STROKES + FRANZ FERDINAND (FIB, Benicassim, 21-22 July 2006)
And, last but not least, the F.I.B. (Festival International of Benicassim) that supposed for me the main access to good live music in the lat decade or so. There has been so many good moments there that I can’t name them here. I’ve selected the 2006 edition because of the “professional” show of the Pixies, the coolness of The Strokes, the enthusiastic performance of Franz Ferdinand and, above all, the long-awaited performance of Morrissey. I did never see The Smiths playing live and the previous show of Morrissey two years before was mysteriously cancelled. But when I heard the first notes of “Panic” it was clear to me. It worth the wait.