There are currently 3 cards banned from a tournament with an unlimited set and they are Neo Genesis Slowking (ability to nullify any trainer), the Birthday Pikachu (kind of like a custom card, which is my guess to why it was banned), and the Ancient Mew (banned for being unreadable). Sneasal for awhile was left banned, but was unbanned after it was nerfed in HS Undaunted.
In Modified Format (which is much more common) you can only use cards released from certain packs, making the above banned without needing a reason anyway. Currently, you can only use cards from Next Destinies and onwards.
Source 1
Source 2