Nitty Gritty Dirt Band, Mr. Bojangles
Like a Rolling Stone was originally a waltz. One of the Dylan anthologies has a recording of a demo in waltz time.
“Someday My Prince Will Come.” For an additional challenge, use a Miles Davis version. 
Try the cover of Manic Depression off the Stone Free album. Seal and Jeff Beck. Little slower pacing.
*Innocent when You Dream * by **Tom Waits ** is a waltz if I recall correctly. Beautiful song too.
2000 Miles by The Pretenders
Norwegian Wood, You’ve Got to Hide Your Love Away and She’s Leaving Home - The Beatles
Cattle Call by Eddy Arnold has been used in a lot of movie soundtracks. You’d likely recognize it if you heard it. (It has a memorable yodeling introduction.)
Dreaming My Dreams With You by Waylon Jennings (later covered by the Cowboy Junkies)
Hollywood Waltz by The Eagles
The Pogues have several:
Navigator
A Pair of Brown Eyes
I’m a Man You Don’t Meet Every Day
The Band Played Waltzing Matilda
Philadelphia Lawyer - Woody Guthrie (Willie Nelson did a nice cover a while back.)
There is a long tradition of waltzes in country music. Dwight Yoakam has produced many fine waltzes, such as:
You’re the One
One More Name
Traveler’s Lantern
Lucky That Way (but this one is…very…slow…)
I first knew this song as done by Manfred Mann on Pretty Flamingo (one of the first albums I ever owned). Their version is in 4/4 time.
I read this post and went 
How is it even possible to do the song in 4/4 time? But then I listened to a snippet at Amazon, and sure enough, you’re right.
I guess Manfred Mann didn’t quite grasp the concept.
“Christmas Don’t Be Late” aka “The Chipmunk Song”, Billboard #1 Single in 1958.
We’re all in the Dance by Feist from the soundtrack Paris Je Tiem
“Tubular Bells” is 3/4, IIRC. The Exorcist soundtrack version should be perfect for Halloween.
Assuming you mean the opening theme (the “Exorcist” music), it’s actually in a compound meter that adds up to 30/8 (7+7+7+9/8). I think you may be hearing those 7s as a “limping” 3/4 (one-and-two-and-three-and-a).
Hmm. Nobody’s mentioned *The Star Spangled Banner .
By “popular” do you mean well-known?
I sort of meant songs from within pop culture, but what I was really getting at was songs that I was likely to already have. It’s also fun to be able to pull songs from odd groups that no one would assume would ever do a waltz. Jimmy Eat World that I mentioned earlier is a sort of punkish, maybe slightly emo band that’s still around, with lots of loud guitars and lead singer that’s not very melodic, so it’s a lot of fun to bring out a waltz from them. Likewise, I’ve just discovered that Sad Songs and Waltzes by Cake is also a waltz.
But I’m quite willing to try almost anything that anyone in here suggests. I’m quite entertained that The Star Spangled Banner is a waltz, and I’ll try that as soon as I can find a recording.
A cherish the vision of a rehearsal hall of dance students waltzing to this.
Metallica’s “Nothing Else Matters” is in some multiple of three over something. (I’m pretty sure it starts in 6/8; it may change in the middle, but it is still waltzable) if you have that lying around.
Pretty Maids All In A Row by The Eagles, too.
Even the heavier part with the distorted gutiar solo is in 6/8.
The Beatles, Baby’s in Black
Waltzes are sometimes hard to sing. On the Beatles Anthology album, John tries to sing “I’ll Be Back” in 3/4 time but gives up in the sing and the final version is in 4/4 time. 