Twenty questions is what is called "a parlor game." They were very popular in the 19th century as after-dinner activities.
The traditional Victorian opening, as I understand it, which didn't count as a question, was "Animal, Mineral or Vegetable?" A hundred years later, that's not a very good opening. What we started using when I was in college and I've passed on to my kids as a better starting place is "Is it or was it ever alive?" That one counts as a question.
Another traditional question is "Is it bigger than a breadbox?"
The Wikipedia entry is well done and has references to the game appearing in A Christmas Carol by Dickens, in "A Goofy Movie," on "Family Guy" and other places.