Can you add to document toolbar, where we have "Split Editor" button, to start of the list, button â–º for "Run Document Code" (not selection)?
You can use icon from debug "Start Debugging".
thank you.
Released in latest version

Can you give a configuration item to let the user decide whether to display this button? It's useless for many people, and the BIG GREEN ICON destroys the color theme. It's a little ugly on 'Solarized Dark' and 'Solarized Light'.
@formulahendry
And, if it possible, can you change it to red square with "Stop" function to kill executed process. Some broken scripts can work very long :)
thank you.
I agree with @Mohanson. I don't want this.
Added option to hide 'Run Code' button:
"code-runner.showRunIconInEditorTitleMenu": false
Also, I make the green icon smaller then before, and #132 to track the refinement of 'Run Code' button

@Mohanson Currently, VS Code does not provide a way to dynamically to show/hide or change the button.
You could use Ctrl+Alt+M, or stop code running in Output Channel

Most helpful comment
Can you give a configuration item to let the user decide whether to display this button? It's useless for many people, and the BIG GREEN ICON destroys the color theme. It's a little ugly on 'Solarized Dark' and 'Solarized Light'.