As far as emotional connection and musicianship? That would have to have been
Zappa Plays Zappa, Melbourne Hamer Hall on 30th November 2007. Dweezil and his group, Ray White and Steve Vai playing many of my favourite Zappa compositions from when I was an impressionable young teenager, amazed by the '
statistical density' of it all. An added icing on the cake was a large projection screen behind the band on stage where for a few songs they had recorded footage of Frank playing, his son playing guitar with him onstage. As I never saw Frank play live before he died, this was the next best thing... I'm not ashamed to say at a few points I had tears (of happiness, nostalgia & sadness that Frank was no longer with us) in my eyes. That's how emotionally powerful it was for me.
Other great gigsI've been to were
Midnight Oil playing at the Astor (Melbourne) ...God, I can't remember when..
The first 'big' concert I ever went to was
ELO in '77 or '78... they played at the Myer Music Bowl and had this incredible laser light show going along with the music... the amphitheatre was open to the night sky so the laser beams were shooting out & up into the night sky.... I'm not sure if we were under any official flight paths, but it could have been a bit dodgy...
I remeber being blown away by the music and spectacle of it all... as another forum member has said in this thread, perhaps there was a certain degree of innocence, naivety, what have you, but I remember it as being brilliant.
Then there was
David Bowie on his Glass Spider Tour in November '87 - that was great, but it was drizzling and they were playing at Kooyong Stadium a tennis stadium in the middle of a blue-ribbon conservative suburb, so the volume levels had to be limited so as not to upset the nearby residents. Sort of defeats the purpose of a live gig if you ask me...but...
I have seen
Hall & Oates,
Peter Gabriel 'So tour',
Genesis...oh and
Gary Numan at the Palais, what a cool show (except I recall the bass player throwing a hissy fit that night, Numan's band may have broken up that night!) ...and so many more. All great in their own ways and for their own reasons. I think when you see a band play live, there are a lot of different factors that affect your experience, not the least of which is your emotional and developmental makeup at the time, where you are in your life, what you are going through. Then there is how much you (mind altering drug of choice) you had imbibed at the time etc...
the only live gig I really didn't appreciate was The Eagles back in '95 or '96, playing at the Tennis Centre. I really only went along because a colleague had some tickets he needed to sell, so I took my then new girlfriend (now wife) along. BORING. They just sat on stools on stage strumming away the same old songs. No passion, no energy, no showmanship. The crowd got really excited when one of them got off his stool and walked from one side of the stage to the other...duh. Melissa Etheridge was the opening act, she should have been the main event. Ha. I remember that we went outside for a good part of the gig to stop from falling asleep, there was a good view of the city and some fresh air from one of the gig's balconies. I taught Jane how to tell the difference between stars and planets in the night sky that night...
no worries. 
but the older kids were asking him questions! I was about 14. 