Not only can’t you dance to this music, it’s been argued that you can’t even listen to it:
(emphasis mine)
I was in a bar once listening to a Rush cover band. They started to play ‘YYZ’, and a couple walked out onto the dance floor. The band actually stopped, and the lead singer said, “What are you doing? You can’t dance to this song! Go sit down.” They did.
Eagles’ ‘Disco Strangler’ would be very hard ro dance to. I suspect it was intentionally written that way. Because disco.
There was a Classic Rock bar in Raleigh in the early nineties. I used to enjoy watching people try to dance to “Paradise by the Dashboard Lights.”
The thought of this is similtaniously terrifying and intriguing.
“Skimbleshanks” in Cats alternates between 4/4 and 13/8 (if I recall correctly). And that show does not lack for dancing. Just seconding that an odd time signature is no obstacle if you know what you’re doing.
I’m thinking about Tom Sawyer and I’m having some real difficulty coming up with a way to dance to it. It’s really more of an ‘air drum kit’ kind of song.
The Crunge isn’t just a song you can’t dance to; it’s a James Brownesque funk song you can’t dance to.
This is one I made up. A work in progress and unrecorded so, alas, performed by my midi robot band, The Gin-Soaked Bar Room Queens.
They were actually really good. I can’t remember their name though. It was close to 40 years ago.
Tom Sawyer is another one that would be very hard to dance to. Rush had a lot of those, as did a lot of prog bands in the 70’s. Stop time, strange time signatures, lots of changes in tempo and time, etc.
Disco was probably the answer to that, given that all she wants to do is dance.
For your viewing pleasure:
I stand delightfully corrected 
In the “Mother/Son Wedding Dance” thread I jokingly suggested “Mother” by The Police, and someone asked “Can you even dance to that?” So I guess that song would be my answer.
Tchaikovsky’s 6th symphony, second mvmt. is in 5/4, but at first listen sounds like a waltz. I think any couple that attempts to waltz to it will be stepping on each other’s feet by the third bar.
Looks as if they’re dancing
For example, here’s a Bulgarian kopanitsa in 11/8:
It really hits its stride at about the minute mark. The beats are short-short-long-short-short, or 2+2+3+2+2. Once you catch on to where the “1” is, you can just count it as 1-2-THREE-4-5, with the three elongated. Trying to actually count “1-2-1-2-1-2-3-1-2-1-2” becomes a bit of a pain in the ass at that tempo.
But it’s danceable and people learn it within the culture. There’s definitely a learning curve to it, and you do have to internalize the beat, but once you get it down, you can follow it. An odd time signature (by Western standards) alone does not make a song undanceable: you just need to adjust your step to it.
In addition to just being creepy as hell, “Mother” is also in 7/4 time, so it’d be difficult to dance to (though, as @pulykamell has suggested, not impossible if one knew what one was doing).
Is there music that cannot be danced to?
How about Gregorian chant?
Hold it–I’m supposed to coordinate my dance movements with a beat? When did that become a thing?
I’m left with either “I can dance to anything” or “whatever I’m doing is not dancing.”
Yeah, for something like that – and I’m not a dancer, more of a swayer – at that tempo I’d do one step of three count with my left, and one step of four count with my right, and land back one the one with my left foot. It actually has a nice sway to it. Or possibly L-R-hold-L-hold-R-hold (quick-slow-slow-slow). I’m sure an actual dancer would be much more creative.