being a jazz fan I can mention many standards. September song in the version made by Red Norvo, Charles Mingus and Tal Farlow. I'll remember april played by George Shearing. I'll be around (Alec Wilder) played by Marian McPartland. Ev'ry time we say goodbye played by Coltrane. Summertime played by Sidney Bechet. Danny boy played by Ted Greene.
Stella by starlight played by Lenny Breau or Genil Castro.
Talking of Beck there's obviously also Cause we've ended as lovers.
I rember having heard many interesting versions of Norvegian wood (I remember especially one played by two acoustic guitarists that was just beautiful, but sadly I don't know who they were) and While my guitar gently weeps.
Anyway, thank you for those video, Herring is a wonderful guitarist.
Bill Frisell has been doing this sort of material often in the last few years. There's Imagine (all Lennon covers), Guitar in the Space Age ( mostly early 60s rock standards) and When You Wish Upon A Star (classic soundtracks -- from the title song to Morricone to Psycho...) His approach is somewhere between jazz and Beck, but with the kinds of entrancing atmospherics that Mr. Bill is so well acclaimed for as additional spice.
Jimmy Herring is a pretty unique player. I don't think there is too much stuff out there like him. Neal Schon had an album out called Voices where he played guitar over pop songs. It sounds awesome, but doesn't sound like Herring.