Simple 2d game
To do app
Timesheet app
Implement a clone of x with something extra of your choosing
Top Twitter celebrity app using its API
Building a search engine
Creating a programming language
An issue with the programming courses at my uni was that none of them used a database. The programs were toy apps by design. Instruct students to use sqlite or MongoDB, and encourage them to use PostgreSQL/MySQL.
Our database class did use databases, but we had no integration of the two subjects.
To do app has always seemed an optimal one to me, since it should be relatively accessible, no matter your prior experience, but infinitely customizable. I remember a YC founder telling me that both pg and sama didn't think there was a broadly available to do app that met their needs, so they both rolled their own (and continue to update it as their needs change). That seems like a pretty optimal intro project to me
Our database class did use databases, but we had no integration of the two subjects.