A very simple application, and my first attempt, is to combine several RSS or Atom feeds and search through them. This is really very amateurish, compared with some people.
The best feature of Pipes is the way the visual editor tells you exactly what types of data are being passed around. Can you connect a "fetch site feed" object to a "filter" object? Yes, because fetch site feed output items, which is the input for filter.
This could make Pipes a great introduction to programming. It demonstrates, in a very visual and safe space, how data is passed from one part of a program to another. This is the same process real programmers use to map out complex software, meliorated for the non-technical.
So your first homework assignment is this: build and publish a Pipe. Post the URL in the comments; I want to see what people make.