The Friend magazine publishes a set of cards with the faces and names of the modern-day Apostles to help children get to know them. There are two cards for each apostle—one with their picture and one with a few facts about the apostle’s life. There is also a set of cards of the women leaders.
The website My Best LDS has created a game using these cards that could be used with a Primary class or with your family. Read a description of the game.
Update May 1, 2016: Here is a link to updated cards with the new General Primary Presidency.