For detailed information about this series, see: Family Basic at Nintendo Wiki
Family Basic is a programming language program for the Famicom that was released in Japan on June 21, 1984 and also included the Famicom Keybord peripherial. A Version 2 was released shortly after, featuring additional elements and features, while Version 3, released on February 21, 1985, added pre-made games, but not all features from Version 2.
Note that being a programming software, Family Basic itself IS NOT considered a fictional series, only those pre-built games in Version 3 are considered fictional works, and for this reason this is called the Family Basic games series.
Links to other series
Note: while Wario game WarioWare, Inc.: Mega Microgame$! features a microgame called "Family Basic", it's only actually based on the Famicom Keybord peripherial and the programming aspects of the software, not the fictional games, so it doesn't count as a link.