There aren’t many songs that really withstand the test of time, and are still frequently sang years after their release. Even popular songs mentioned above (such as Racheim) aren’t used much anymore. Here are some that I believe have withstood the test:
Acheinu (actually from Lev v’Nefesh, not from Dveykus, although still Abie Rottenberg)
Hamalach Hagoel (Dveykus 4)
Shalom Aleichem (Regesh 3)
V’zakeini (Baruch Levine)
Machnisei Rachamim (I believe originally from Shlomo Simcha?)
Just One Shabbos (MBD)
Mama Rochel (Journeys)
Memories (Journeys)