How can I hide the line numbers in Notepad++?

This option controls the visibility of line numbers: Settings → Preferences → Editing

I'm on version 7.9.2 and the answer is slighly different than @Der Hochstapler's answer from 2012.

For version 7.9.2 and later go to Settings → Preferences → Margins/Border/Edge and there's an option to display Line Number as shown:

Also, I was going to add this as a comment but since I don't have 50 reputation it's now an answer. I do not even have enough rep to display the image above, you'll just have to click it.

If you have the Status Bar displayed when your doc is open, select the View tab and uncheck Line Numbers and the numbers should no longer display. Short cut would be to click on your doc, then hold Ctrl-Shift-N keys to toggle between numbers and no numbers.