The Votomatic system was a punched card based voting system that was still in use by 2000. This stretches the scope of your question a little because the punching mechanism was a sort of push pin that dislodged a previously perforated chad. But they were definitely punched cards.
Recounts were a nightmare, especially in Florida, where discerning the intent of the voter was problematic, when a chad was not completely pushed out.
You can read up on it in Wikipedia