Mid '90s, a friend suggested we go to see Betty Carter at Ronnie Scott's. I didn't really know her. Surprisingly for a massive jazz fan who lived in reach of London he'd never been to Ronnie's, so he was amazed when we were seated right in front of the stage - which back before the smoking ban was where the non-smoking seats were.
Carter used to hire young local bands when she toured, and I can't remember who any of them were unfortunately, but she really made them sweat, and we were close enough to see the terror in their eyes! They did well though.
Melody Gardot at the Lowry in about 2010 was also pretty amazing - at one point she did Somewhere Over the Rainbow as a duet with her cellist, in which he strummed the cello across his knee like a guitar. (Somehow, inexplicably to me, my wife deduced from this that they were in a relationship - clearly a level of intuition reserved for either women or classical string players.)
I don't want to nominate a worst, but I do remember being disappointed with Björk in Manchester in probably 1999 - I guess I had high expectations because it was Björk but she basically just ran through the tracks on her current album, which sounded like they did on her current album. I believe this was the period she was dealing with a serious stalker though so maybe her heart wasn't in it.