So I want to build a home server to use as a media server, and to back up my photos etc.

I am also currently doing an online course, and happen to spend some time at work as well as at home working on it. I don't like using Google where I can help it, but I find google docs really useful. So I'm wondering if there's an open source application that works essentially the same, but I could run off my own server? It would have to be web-based as I use Windows at work and can't install new programs :/

edit: Thanks everyone for your suggestions! I've got quite a few leads to follow now, it should be fun!