Joni Mitchell wrote River after she ended her relationship with English singer Graham Nash. She was living in Laurel Canyon, Los Angeles – hence the line "It don’t snow here, it stays pretty green" – but in the song she dreams of escaping from her remorse on one of the frozen rivers of her Canadian childhood.
Her original recording, on her 1971 album Blue, is flawless. However, the only available video of her performing the song live is from 2008, with jazz pianist Herbie Hancock; it's a very different kettle of fish, which you will probably either love or hate.
Because of the song's lyrical and musical references to Christmas, it has become a favourite for solo singers to include on their Christmas albums. Some of these performances are more than competent (Cee Lo Green's, for example), but still somehow fail to match the musical and emotional purity of Joni's original. Australian folkie Angus Stone's version seems to work better because he plays it on the guitar rather than the piano, drops the Jingle Bells motif and generally does his own thing with the song.
Interestingly, River seems to work quite comfortably in a group or choral setting, where it can become less of a personal statement and just be a good song to sing. There is a nice trio performance by Nashville singers Megan Davies, Emily Hackett & Keelan Donovan. Neither of the lead singers has to own the song, and the harmonies help to put the performance at a comfortable distance from Joni Mitchell's original.
Much less polished, but with a good multi-part arrangement, is this performance by the young CHS Choir.
Lastly, the left-field performance: renowned American banjo player Béla Fleck manages to combine in his instrumental version both the vocal melody and some of the piano fills from the original, and on this much-maligned instrument conveys the song’s sense of regret just as acutely as any of the vocal cover versions.