Need Father's Day Gift Ideas? We celebrate the life of our Fathers every third Sunday in June. What are the best gifts for this occasion? That would depend on your father and what he likes to do. After all, no two fathers are alike. Give your dad something on Father's Day that shows how special he is, such as a mp3 recorder, wine set, corkscrew, wallet, money clip, cuff links, shoe shine kit, key ring, picture frame or decorative chess set.