associated as in happens to ballroom dancers more frequently than with other dancers, athletes, and normal people? Or how injuries(which are not necessarily caused by ballroom dancing) can interfere with dancing?
Besides what latingal has said, also plantar fasciitis has been popular. I've also had shin splints on and off(but that could also be from tracking and field). Others include twisted knees and ankle injuries. I haven't seen anyone get a torn ACL yet, but I would imagine it's likely. There's also incidence of concussion from a collision where two couples spun into each other. Feet problems include common blisters(and blood blisters!) and ripped off toe nails. Various fungi and athletes foot as well.
Many years ago I did tear myy ACL doing tango. I chose physical therapy over surgery and have never had a problem since.
From my own oberservation of top professionals who have had knee surgery, both ballroom and latin play havoc on knees. Personally I also have knee problems, but I think mine are due to age and arthritis, but as professionals far younger than I have had knee surgery, there is obviously a lot of stress there.
My partner has had a few shoulder / rotator cuff problems from incorrect leads when she's danced with others in a group class or social setting. Thankfully they weren't permanent, but she was sore for almost a week in one instance.
Personally I haven't (yet) experienced many injuries or pain. Back when we were new to dancing, what hurt the most was finding those muscles in our legs and arms we'd never had to use before. That went away with practice.
And of course breaking in a brand new pair of dance shoes (Ow toes! Ow feet!)
I just re-injured my bad ankle for the nth time today dancing rounds. I don't know what it was, we were on our second round and just setting up for the waltz and I felt something pop. I danced the round, but by the time I drove home the ankle was swollen and painful. I'm icing it now.
My back has actually gotten better since I started ballroom dancing. I still do get lower back pain sometimes, but not like I used to (serious compression injuries from repeated falls as a horseback rider.) It does, however, have a tendency to aggravate my bad knee. I dislocated and fractured my right knee when I was fourteen, and it's missing a lot of cartilage now. For some reason, Smooth and Latin seem to aggravate it the most, though it's also not fond of Bolero.