I'd like need to drag and drop heaps of texts between documents, and rather copy only the text, without formatting. Is there any way, for example by pressing some modifier key while releasing the mouse button?
I don't know which application you are using but in Pages the simplest way is to use Paste And Match Style
Under the Edit menu
is the keyboard shortcut
So if you are pasting into a document that has no styles set it will be pasted in as the standard body
Different applications may or may not have the same functionality. I don't have MS Word on my machine so have no idea if this is the same for that application for example.