There’s too many categories really but:
Best energy: Motorhead does it almost every time, I think I’ve seen them 7-8 times now and only one was even remotly bad.
Best musical/stage performance: Iron Maiden, they usually play/sound the best. Rush would be a close second though.
Gets into it the most: Dee Snider, every time I’ve seen this guy he’s really into the music, can’t wait until Twisted Sister gets back together.
Warren Zevon Whether with or without a band, the man plays magnificent music magnificently
The Who '70, in a tiny sweaty venue in Denver. Shook hands with Pete, which was pretty cool, I was just a teenybopper
Jethro Tull same venue, same year, Ian Anderson pranced in his codpiece and kicked butt with his flute
The Doors '70 Morrison was drunk, but he was very entertaining in his drunkenness
The Grateful Dead '72 Those guys were at their height then, it was a long dreamy afternoon, and they threw out ounces of pot in neat baggies complete with matches and papers
Marvin Gaye '73 What a voice. It was my 18th birthday and I felt like he was singing to me.
Neil Young '78 The Rust Never Sleeps Tour. By far the best concert I ever, ever experienced.
Young again at Red Rocks in 2001: just experiencing his Cowgirl in the Sand encore in the wind and the rain was worth the price of admission.
Springsteen '78 at Red Rocks, playing his heart out, he really did prove it all night long
The best show I ever saw was Peter Gabriel at the Forest Hills Tennis Stadium, back in 1982 or so… the “Security” tour. Great songs, very stylishly presented and cleverly choreographed.
Sesame Street Live, early nineties. I forget the actual date, but I was young.
Best concert ever. 
Oingo Boingo, at the Hollywood Palladium, in 1988. General admission, dance-hall mayhem. God I wish they’d never broken up. Their last album was brilliant.
Runners-up:
Big Bad Voodoo Daddy and Cherry Poppin’ Daddies, someplace in Hollywood, in 1998 or so.
Bauhaus, at the Hollywood Palladium, in 2000 (I think). Great performance and cool just for the “my god, that’s Bauhaus!” factor.
Front242, Spahn Ranch, and Projekt Pitchfork at the Ventura Theatre, 1999. What can I say? I love evil.
U2, with Garbage opening up… wonderful concert…
Anyone who got to see Pink Floyd, the Clash or the Ramones, I envy you. My favorites have to be Sigur Ros, Flaming Lips, the White Stripes and the Datsuns before they blew up, and Radiohead of course.
There have been a number of 'em, including being in the front row for Cream in a tent, but I’d have to say Little Feat around '74 at the Main Point in Bryn Mawr.
It was about a 200 capacity coffee house venue.
Feat came on about 9, tore the place up till about 11, came back did an encore for about a half hour, came back did another encore for a half hour, came back did another song, started to leave the stage and Billy Payne says, “Hey, we’re having a good time. You don’t mind if we just boogie for a while, do ya?”
They kept playing till about 3am or so. What a night!
I saw the Sex Pistols at Winterland in San Francisco in January of 1978. It was their last show ever. I’m not sure if it’s the best show I’ve ever been too, but it was memorable. I think the show before that one was in San Antonio, and I guess that one was pretty wild. They were kind of burnt by the time they got to San Francisco.
The best, from a perfomance point of view was Blue Oyster Cult at the Cow Palace in 1977. Full force. Not a minute of down time.
Clash, Cramps, and Dead Kennedys on the same bill at Kezar Pavilion in San Fran in 1979 or maybe it was early 1980, can’t remember. Jello Biafra dived into the audience and was nearly torn to pieces. Those were the days.
Bob Dylan with Tom Petty and the Heartbreakers back in the mid 80s at Alpine Valley, WI was a kick-ass show.
The Replacements in this dive theater in Green Bay (1989ish?). The Goo-Goo Dolls opened for them before anyone really knew who they were. They were prety good, too. But the 'Mats absolutely rocked that night.
As I’ve gotten more mellow in my recent years, I’ve gotta say that one of the best concerts I’ve been to lately was Lyle Lovett (with his large band) in Madison a couple years ago.
Going to be a repeater here, but Springsteen, last year. Yes, I came late to the Springsteen bandwagon, but I lucked upon seats behind the stage, very close to the band. I was given a crash course in everything Springsteen, and on the night of the concert, Bruce came to the back to sing to us… I jumped around and waved (note that this was during a relatively quiet moment), and he looked directly at me and winked. Yeah, best concert ever.
Sigur Ros in November
Cursive, every time i see them(3)
NIN in 2000
Thursday in October
Pigface december 2001
Rammstein, every time i see them(3)
Just about every time I see a concert, it’s my favorite until the next one comes along. The last show I went to was AFI in April of this year, which was pretty impressive. Except for losing my cell phone and $20 somewhere along the way. It was an extremely energetic show and I even got to meet the band beforehand.
I would say Paul Simon, but Brian Wilson opened for him, and it was really awful. So that leaves Paul McCartney—it was the most amazing experience of my life. Almost spiritual.
I’m going to see Ghost of the Robot on Saturday though, which means I’ll be in the same room as James Marsters. I have a feeling that’s going to be another spiritual experience.
Best by far, hands down, Simon & Garfunkel at Carnegie Hall circa 1967. Just before Bookends came out.
Most memorable include:
**Doors**, circa 1967/68, at of all places Staples High School in Westport, Connecticut. Went down and stood by the stage right in front of Morrison. He was drunk/stoned/whatever, and other than nearly losing my fingers when he nearly stomped on them, the most amazing thing was looking in his eyes from about five feet away and realizing that he was DEAD inside. I've never seen such empty eyes. Still gives me chills.
**Incredible String Band** at the Filmore East in NYC circa 1968/69. Don't remember much of the show, got a contact high just breathing. :D
Once again, Staples High School, circa 1966/67. Somebody or other was supposed to play (some kid's parent had major agent contacts and for two years we had a series of brand-new hit groups performing -- Doors, Rascals, Yardbirds, Cream (!!) -- in this high school auditorium, very surreal), and was several hours late because they were busy watching their tapes of themselves on the Ed Sullivan show. So they got this totally unknown guy out of the Village who came out and for three hours sang, did standup, and performed a song that he hoped would be a hit. It was. It was **Richie Havens**, and a year later he was opening his Woodstock set with that song. (He was so great that when the main act finally condescended to show up, at least a third of us got up and walked out ostentatiously!)
Most memorable concert I didn’t go to:
**Beatles**, their last American tour. WON a front-row ticket to their Seattle concert. I was 13 years old. My father made me go CAMPING instead. Gave the ticket to a girlfriend. She TOUCHED Paul McCartney, she was so close to the stage. My father went to his grave unforgiven for THAT one.....Pink Floyd, '72 or '73 - at the Auditorium in Chicago. Man-o-man, what a show! I don’t think you ever quite get over it. I wish you all were there.
For major concert events I’d list these:
Grateful Dead, Ventura County Fairgrounds. I think it was '83 or '84, but I don’t remember so well. 
Also Genesis in the 70’s when Peter Gabriel was still with them, and long before they became mega-pop sellouts.
Rolling Stones, at the Los Angeles Coliseum. It was the Tattoo You tour. Good show, but I thought Jagger looked stupid in the American football pants, and that he also shouldn’t have bothered picking up a guitar with Ron and Keith in the band.
But my most enjoyable musical experiences have been in more intimate settings. Jorma Kaukonen, J.J Cale, and Chuck Berry at the Roxy in Los Angeles, various dates. Flaming Groovies at the Whiskey-A-Go-Go, when it was still a comfortable club with tables and chairs.
And best of all, Quiet Riot at the Whiskey, several times in the late 1970’s when Randy Rhoads was still with them.
Of my rather uninspired concertgoing experiences, I’ve got 2 that I’d count as the best:
Soundgarden - 1994, Nautica Stage, Cleveland.
This was my first concert, and it was incredible. They sounded great, had cool visuals in the background, and because the venue is so small, it felt very personal. Fantastic show through and through, and it was especially cool when the rain finally stopped during the playing of “Black Hole Sun.”
Toad the Wet Sprocket - 1997 (I think) - Odeon, Cleveland.
I saw Toad 3 times…Blossom Music Center in Akron in '95, at College in NY in '97, and a month or two later at the Odeon. The third performance was by far the best. They just rocked that night, and I managed to get to within 2 rows of the stage. ‘Come Back Down’ was the highlight of the night, as Glen just played and sang with a spotlight on just him from above. Awesome.
My most unique experience was being backstage with the band before and after a Stephen Stills concert in CT a few years ago. I’m friends with a guy in the band, so he brought me out and I rode in the limo with the band as we went to the show and at dinner with them. I had my all access pass and helped set up the stage. We hung out in the dressing room and ate nearly all the food that was intended for Stills. It was pretty cool, even when I was introduced to Stephen Stills and he just said “Hey…” and then ignored me. The rest of the band was really cool, though.
Metallica in the SFX in Dublin around 1986/87 (Master of Puppets Tour, I think). The place was so small they couldn’t fit their stage set in. They absolutely blew the place apart.
Ozzy in the Top Hat in Dublin around the same time. It was advertised as a ‘live rehearsal’ but it was a straight ahead gig, again in a very small venue. I went home a very happy drink-addled teenager.
Van Morrisson in Semple Stadium in Thurles in 1991 was another highlight. He wasn’t his usual grumpy little bollix self and did a fantastic set.