I am an amateur, so maybe my suggestions are a bit basic for more experienced animators, but to start it would be good to practice things like:

• Picking up objects, and looking like they have weight to them
  
• Throwing objects and having them collide realistically with characters or the environment
  
• Having a character fight with another character and look like they are reacting naturally to hits they receive.

Sorry if this is a bit boring, if I think of more interesting ones I'll post them.

Hey man, these ideas aren't basic (especially the fighting choreography).

These are good ideas, but the character fighting is very advanced.

The first two would make a great challenge because they teach two key principal rules of animation:

1. Squash and Stretch
   
2. Anticipation

Fighting choreography is heavily reliant on understanding those two, as well as Staging, Follow Through and Overlapping Action, Slow in Slow out and Secondary Action. If you do want to try and experiment then I suggest rotoscoping an old Jackie Chan movie fight scene.

Sorry for the late reply!
Hmm, you're right I probably got a bit ahead of myself with the fighting animations, heh. I might put that aside for now.

Yeah, a challenge based on those first two principals does sound good, it could be open to people at any skill level.

It could be as simple as two characters throwing stuff at each other for about 15-20 seconds - the objects can be as heavy or as light as the animator is comfortable with. Obviously, there wouldn't be much story there, but it would be good practice :)

Hey yeah. I was thinking maybe copying " 11 seconds club ", where the challanges are providing with voice clips,

OR

scenes in which the layout is open for creativity. f.eks "use the box in the scene to create a short animation", or "This character is hanging from the ceiling, animate what happens next".