How do I disable links in Notepad++?

You have to uncheck this option:

Settings » Preferences » MISC » Clickable Link Settings

Once you've changed the setting, you will need to reopen the file in Notepad++ (or restart the application) for it to take effect.

As a Windows 10 user, I found that I needed to run Notepad++ as an administrator in order for this setting to "take". This is probably true for other versions of Windows.

I discovered this after several attempts to uncheck the Clickable Link Settings checkbox. After restarting Notepad++ several times and finding the checkbox still checked, I found this solution from searching Google.