"The World Spins" is a beautifully sad song by Julee Cruise, complete with melancholic traces of the main theme. Its use in Episode 14 adds enormous poignancy to Maddie's brutal death at the hands of BOB.
"Sycamore Trees". It's dark, melancholic tone fits the Black Lodge like a glove, and appearing in Twin Peaks had a hand in reviving the career of singer Jimmy Scott.
Shadows by Chromatics that plays at the end of the second episode of the revival. After the first two episodes withholding music almost entirely, the mellow dream-pop sound is a perfect release of tension, with the melancholy lyrics ("For the last time ... for the last time") underscoring the nostalgia of the show's return.
"The Fireman", from The Return's infamous Part 8. In contrast to the chaotic Mind Screw and Nightmare Fuel prevalent in most of the episode, this music beautifully underscores the serene scene where Laura Palmer is created by the Fireman to counterbalance the emergence of BOB. Peaceful and brimming with hope and optimism, it's already being considered one of Angelo Badalamenti's greatest musical compositions, if not his absolute best.