How many Catholics believe in Transubstantiation? Have there ever been any studies or surveys of reasonably significant size that indicate how many Catholics believe in transubstantiation or would at least claim that they do?
Pew research does some awesome polls on questions like this.  


  About half of those polled (52%) say, incorrectly, that Catholicism
  teaches that the bread and wine used for Communion are symbols of the
  body and blood of Jesus. Just four-in-ten people correctly answer
  that, according to the Catholic Church, the bread and wine actually
  become the body and blood of Jesus. Even many Catholics are unaware of
  their church’s teaching on this topic; while 55% of Catholics get the
  question right, more than four-in-ten Catholics (41%) say the church
  teaches that the bread and wine are symbols of Christ’s body and
  blood, and 3% say they do not know what the church’s teaching is.
  Still, Catholics perform better on this question than does any other
  religious group. 


-Pew Research Who Knows What About Religion

Also this site made a nice graphic.  

In conclusion I think it's safe to say that about 40-50% of Catholics believe in the real presence.  I hope that helps!