Excellent question! While I can think of a few techniques you could demonstrate, other people have already come up with some great resources, so I’m going to mention them first:

I think Kate Compton’s So You Want To Build A Generator is a great starting point for this: a good overview over common approaches, and a discussion of possibilities. (Also available as a PDF).

Her ProcJam2015 talk is also relevant, particularly the practical advice about data structures and using an array of numbers to connect generators together.

Speaking of Kate, her cut-and-play suppliment for Seeds vol. 1 is a generator idea generator, which is a fun way to come up with new ideas to explore.

Casey Reas, one of the creators of Processing, built a series of artworks out of simple, elementary parts. Processing, in general, has been used for a lot of generative things. The recently re-launched openprocessing.org has a ton of examples for inspiration.

Anders Hoff’s ongoing essays On Generative Algorithms and Shepherding Random Numbers are also great because they have breakdowns of the artistic process behind creating new generators, showing how concepts are built up from basic parts.

For some specific use cases, here’s some ideas:

• Creating spaceships, through simple extrusion and adding greebles
  
• Generating cute creatures
  
• Adding new verses to The Twelve Days of Christmas
• Or just combining every Christmas Carol
  
• Using neural networks to train race cars
  
• Flocking simulations
• Telling the story of solving a puzzle or playing a game
• Generating buildings (or entire cities)
• Generating music or sound effects

You may also want to look up the work of pioneering computer artists like Frieder Nake and Vera Molnár.

In addition to Processing, Tracery and Cheap Bots Done Quick are some accessible tools for people to use to start creating their own generators.

Dungeon generation is its own, giant subject: creating better dungeons with cycles, lock-and-key systems, or more narrative approaches are a few of the possible improvements.

And don’t forget to check out the history of analogue generative systems, making a generator out of paper, pencils, and dice can be an accessible, hands-on way to introduce the concepts to people.

Hope this helps!