I'm using the tiling WM i3 and it seems like lots of things in juce are seen as separate windows, hence get tiled.
Affected things are:
a blue 'j' logo in the JuceDemo
Menus (yes, the menubar thing, click on anything there -> new window)
Dragged items (drag and drop)
This feels really odd and IMHO shouldn't happen. My tiling WM is rather obscure ("i3"), but I've never seen anything like that with any other widget toolkit, so I'm rather sure this is due to some juce implementation detail. I haven't tested it, but I'd guess that other tiling WMs behave similarly.
If you want to see screenshots or similar, just tell me.