Not sure if you mean songs I've heard performed live that were really great, or live recordings that sounded great, or some mixture of both.
The one that sticks out for me that I actually witnessed with my own eyes is Thee Silver Mt. Zion Memorial Orchestra & Tra-La-La Band playing "There's a River in the Valley Made of Melting Snow", June 1st 2006 at the ABC2 in Glasgow (I remember because we moved out of our flat three days earlier so I had to come through from Perth for the gig even though a week earlier I was living literally three minutes away from the venue).
At the time the one Silver Mt. Zion release I did not have was the "Little Lightning Paw" EP, which I bought at the end of the show. Now this EP is something of an oddity, containing four new tracks recorded primarily by vocalist Efrim in a stripped-down demo kind of way, and then Efrim in his infinite wisdom decided to play the finished result back on a cheap ghetto blaster and record it playing with a microphone in the room and THAT is the actual audio on the release. The result is a very strange lofi kind of effect that does work, but is kind of frustrating.
So anyway, the last track on this record is "There's a River in the Valley Made of Melting Snow", and the first time I heard it was as the last song of the set that night, and it was one of the most incredible most beautiful moments I have ever experienced. The full scale version they do live completely blossoms out of a distorted tinny and slightly distant-sounding demo into a beautifully intimate song about hope+joy+love+light and all other kinds of Silver Mt. Zion hallmarks.
I was therefore somewhat disappointed by the record version when I actually listened to it.
On a live album though, I'd say the version of "Psycho Killer" on the soundtrack to Talking Heads' Stop Making Sense concert film, with David Byrne doing the song with a simple synth drum beat and an acoustic guitar. A lot of the early Talking Heads studio stuff suffered from the production style of the day, sounding sparse and slightly too airy by today's standards, but Stop Making Sense has a much broader filled-out sound. This version of Psycho Killer is, for my money, the definitive version.
Plus, I have a massive boner for David Byrne's dancing.