An idea I've had kicking around for a few years now is an app that presents famous artworks in the context of time and place.
For people like myself who like great art but have very little knowledge about the relationships or even chronology of the various movements, it would be great to have a broad range of artworks representative of the various movements placed on a map. Together with a slider type interface to choose time periods I think you could get a really good idea of how and when the different movements evolved and how they relate to each other. You could easily see for instance that there wasn't much happening in city x in a particular decade but a lot going on in city y. Move forward a decade and while y might be in decline, you can easily see that city z is becoming active - and that the newer works have clearly been influenced by what was happening in city y a decade earlier.
I have a fairly clear idea of how something like this could be monetised, together with how to get the necessary content. Haven't given much thought to how it might be marketed though. You could call it 'Art in Space and Time' (artisat).
I like that it presents a great challenge from a UI perspective - it could be done really well or really badly.
Anyhow, work keeps getting in the way...
If anyone likes the idea, go for it. Get in touch if you'd like to hear a little more - I might even be willing to get involved.