My first project, done during my coding bootcamp with The Tech Academy (Portland, OR), was a cute little sea shanty sing-along app. It would play a song for you and show you the lyrics, and give some details on the historical background of the song.
This app used a MySQL database. I created a form which I could use to input new songs into the database which would then display in the app.
The whole app was just a basic Django implementaton, an example of the Model-View-Controller (MVC) design pattern of web apps.
My internship involved work on an actual in-production website for Theatre Vertigo, a local independent theatre club. I added some functionality to the site, including the ability to add events to a calendar.
This was another web app, built in ASP.NET, written in C#. It used a code-first database; here you can see the table I built for my calendar app implementation.
And here's a fun thing I built entirely on my own -- it's a camera controller, which manipulates a pan-tilt-zoom camera and shows a live feed of what it sees. It features pre-set locations that you can click on in the panoramic image, which it will move to on its own. This app works on desktop or on mobile, and is currently in use with several cameras in my home town.