Ctrl+A and DEL (or Backspace) works for me (in Windows). I am using the Wolfram Cloud. I also do Evaluation->ResetSession to reset the cell output numbers.

Alexey, thanks for pointing the cross-post out. Because it is on hold and can be closed in future we are riposting explicitly the answers.

Alexey Popkov

This is very efficient for large Notebooks:

NotebookPut[Notebook[{}], EvaluationNotebook[]];

(simple replacement of the evaluation notebook with blank notebook).

I have tested this method with a Notebook of size 976 Mb containing 36031 Cells and it was cleared out in no time, while the NotebookDelete[Cells[]] method seems to take forever for this Notebook!

Mr.Wizard

This will delete everything in the evaluation Notebook:

NotebookDelete[Cells[]]

This will generate a Palette Button that deletes everything is the selected Notebook:

CreatePalette @ Button["Clear Notebook", NotebookDelete @ Cells @ InputNotebook[]]

As noted in the comments it is probably just as fast, if not faster, to simply Select All and Clear (Ctrl+A and Delete in Windows).

leosenko

If you mean screen, then ctrl + A to select all cells and then hit del. If you mean memory, then ClearAll["Global`*"] if it does not help, restart...

Yeah buddy, thanks