If you have automatic updates enabled in Windows, you will eventually notice a new Icon in the task bar that offers you Windows 10 for free. What if you do not want this notification?

Here is a simple and clean way to remove this notification:
Uninstall the Update KB3035583. You can do this manually by executing a lot of clicks, or just use this command (you need to execute it as administrator):

WUSA /UNINSTALL /KB:3035583

If you want to automate this process, I have written a bash file that first obtains admin rights and then executes the command:

@echo off

:: BatchGotAdmin
:-------------------------------------
>nul 2>&1 "%SYSTEMROOT%\system32\cacls.exe" "%SYSTEMROOT%\system32\config\system"

if '%errorlevel%' NEQ '0' (
    goto UACPrompt
) else ( goto gotAdmin )

:UACPrompt
    echo Set UAC = CreateObject^("Shell.Application"^) > "%temp%\ga.vbs"
    set params = %*:"=""
    echo UAC.ShellExecute "%~s0", "%params%", "", "runas", 1 >> "%temp%\ga.vbs"

    "%temp%\getadmin.vbs"
    exit /B

:gotAdmin
    if exist "%temp%\ga.vbs" ( del "%temp%\ga.vbs" )
    pushd "%CD%"
    CD /D "%~dp0"
:--------------------------------------

WUSA /UNINSTALL /KB:3035583

You can download the Windows10 Notification Remover batch file here.

Update (22.06.2015): You can also disable the update notification by adding this key to the registry:

Windows Registry Editor Version 5.00

[HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\Windows\Gwx]
"DisableGwx"=dword:00000001

Just save this to a file with .reg ending, execute it and reboot. Now the notification as well as the GWX program running in the Background are gone.