"Skaters' Waltz" by French composer Emile Waldteufel and "Swan Lake Waltz" by famous Russian composer Pyotr Ilyich Tchaikovsky both provide traditional waltz rhythms suitable for dancing. "Valser Dans L'ombre," recorded by Lucienne Delyle in 1938 and set to the tune of "Auld Lang Syne," offers a straightforward, stable tempo that's easy to waltz to.
Waltzing songs don't have to be classical. Although most modern songs set in 3/4 time aren't explicitly named waltzes, their time signature makes them modern waltzes. Modern songs set in 3/4 time include "Here We Go" by Jon Brion, "Gravity" by John Mayer, "You and Me" by Lifehouse, "Come Away With Me" by Nora Jones and "If I Knew Then" by Lady Antebellum. "First and Last Waltz" by Nickel Creek and "Dark Waltz" by Hayley Westenra also make good waltzing choices.
The clear beat and moderate tempo of the 1930 recording of "Dancing With Tears in My Eyes" by Ben Selvin & His Orchestra make it a good waltz choice for even those new to dancing.
For Harry Potter fans, the song "Neville's Waltz" by Patrick Doyle is a great waltzing option. "Waltzing With Bears" by Tommy Makem and "Rainbow Connection" from "The Muppet Movie" provide lighthearted but still very danceable waltz options.