I believe he set the restriction so you wont be going through a process of building something simple with a database. He wants something different.
Mine was a chess playing Lego robot. Although there was no database involved it was something unique.
You could still do a web-application that will do something specific. You don't need a database for those, you just need to find something that needs experimenting. It is not essential in completing your project ( although it would be nice ) but you must show the work you have done, the obstacles you have faced and what needs to be done next in order to be finished.
Also he said no database. So you can still save some basic stuff in a text file or XML file.
But it is up to you, what you feel comfortable with.
If you are good with css,ajax etc you can do some jquery fancy stuff to display something.
If you are good with c/c++ you can do an opengl world.
Find your strong points and build something there.