For those ending up with duplicate entries after following John Swaringen's or Laurie Stearn's, like Aske B, this is because these answers are incomplete and don't deal with the removal of the default entry. If you compare them to Steve's answer, they pick up where he says "Now we re-create it" and you still have to do the stuff he says before that to remove the default entry. You don't have to reinstall N++, though you can if you feel more comfortable doing that. Unfortunately, while a .reg file could be created to remove the default entry automatically, to make it easier for those who prefer not to do manual registry edits, it's not likely to work well, since it's probably in a different location for different people. Mine, for example, was in [HKEY_CLASSES_ROOT\CLSID{B298D29A-A6ED-11DE-BA8C-A68E55D89593}].
Another tidbit: If you want to change the location of the entry in the right-click menu, whether to make it be right under the top/default "Open" or "Open with" entry" (and keep in mind it may be when you create it but that may change later if/when another program creates a new entry, so you may want to just do this now to prevent that from happening later) or to move it down closer to the default entry's position (toward the bottom of the top section), you do this via the key name. For example, keys in this order will result in context menu entries in the same order:
[HKEY_CLASSES_ROOT*\shell\!EditWithNotepad]
[HKEY_CLASSES_ROOT*\shell\AEditWithNotepad]
[HKEY_CLASSES_ROOT*\shell\AnotherProgram]
[HKEY_CLASSES_ROOT*\shell\EditWithNotepad]
[HKEY_CLASSES_ROOT*\shell\OpenWithNotepad]
[HKEY_CLASSES_ROOT*\shell\SomeOtherProgram]
[HKEY_CLASSES_ROOT*\shell\ZOpenWithNotepad]
Keep in mind these are merely the key names, and they have no impact on the entries' text, only their positions. The actual text of the entry is determined by the "(Default)" name provided in the right pane. And, of course, you can use this to change the order of the other entries as well (top section only, though I'm sure the other sections can be tweaked elsewhere in the registry, plus I believe there are programs specifically for modifying the context menu.