In no particular order:
1) One – Released by U2 in 1991 as a track on their popular Achtung Baby album. One was written during a time that the band was considering breaking up and allegedly the song brought them back together. You can feel the anguish and hopefulness in the song.
2) Let It Be – Written and released by the Beatles in 1970, as a track on the album of the same name. This song predates me by about 10 years, but it immediately registered with me the first time I heard it. I think that it is hard to find a song more timeless than Let It Be.
3) The Times They Are A-Changin’ – Written and released by Bob Dylan in 1964, as the title track of his album of the same name. Dylan intentionally wrote this song as an anthem for the times. I don’t think that he realized how universal it would become.
4) Piano Man – Billy Joel’s first single released in 1973. I don’t think I have heard any other song that tells a story in the same way as this one. When I hear it, I can visualize being in a bar listening to Billy skillfully play the piano and riff on the harmonica.
5) Ashokan Farewell – An instrumental piece composed by folk musician Jay Ungar in 1982. Popularized by the PBS television miniseries The Civil War. Many people mistakenly believe that this song was from the Civil War because it so elegantly captures the spirit of that period.