Doing all these challenges, I would really like to see challenge Tuesday come back. Does anyone have any great ideas for what challenges we can host?

Some ideas:

I'd like to see some white PVP duels, or level 1 duels.
All blue items MP1 Inferno challenges.
Time Trials from level 1 to end point, differing MP levels.
Hardcore leveling competitions, most levels in shortest amount of time.
Legendary competitions
Whimsyshire team competitions
Budget builds (100k) competitions.

or this.

What about challenges for largest kill streak or killed with a single blow, or objects smashed?

@tsukiyomi

I think those have all been covered in the past, but with the new monster densities it might be fun to redo them.

Ah I must not have been here for that, what kind of challenges have already been done?

I think I agree they would definitely be fun to redo with the new monster densities, I'm still exploring sections trying to figure out what has the best density after the last patch.