For me, the quintessential example of this is Bob Malone. I first saw him several times at a folk festival, and he electrified me each time. I thought I had a new favorite artist, and bought a whole bunch of his albums, only to realize that after the second playing I never wanted to hear his those CDs again.
And yet I still check constantly to see if he's coming to near where I am, because I absolutely would go to another concert of his in a heartbeat. Every year when I go to folk festivals, and they ask who wasn't there that I'd like to see, if Bob Malone isn't there, I write down his name. He's amazing live.
Here's some of his live songs. They fail to capture some the effects of watching him live (he has serious charisma) but they're still musically far better than recordings I have on his CDs.
The only pre-recorded song I can find on YouTube is actually at about the same level as his live recordings, but I'm not in the least bit surprised that it's the only one I can find. For the most part, it seems like live Malone and CD Malone are practically different artists.
What about you guys? Are there any musicians you really love live who can't seem to make a decent CD?