Yes, there are plenty of these cards! A lot of these cards were given out for Japanese-exclusive promotional events or tournaments. Here are the rarest and most notable of these cards, although I'm sure there are plenty more.
The Pikachu Illustrator Card (The rarest Pokemon card, given out as a prize for a CoroCoro art contest in Japan)
Japan World Championship Master Key Card (Given out at the 2010 Pokemon World championships in Japan)
Magikarp Trophy Card (Given out to Japanese University students who answered correctly on a specific test.)
Tropical Mega Battle Lucky Stadium Card (Given out in the year 2000 to participants in summer tournaments, throughout different locations.)
Kangaskhan Family Event Trophy Card (Given out to families with the most points in a tournament where families battled other families with Pokemon cards)
These are of course a few of the most notable ones, as there are many, many more which have little explanation, and are not worth mentioning. If you'd like to read about more of these cards however, this may help you find more information: Full list of Japanese promotional cards
I hope this answered your question!