The only editor I've found that reliably does that is mousepad. (I believe it's from xfce4) It's also really fast to start like Notepad++. Though it is more like windows Notepad in features than a bigger editor/ide.
Also:
* instead of giving an error message when it lacks permission to read a file (like mousepad) it instead prompts for credentials and attempts to open the file.
* it lets you put the tabs on either side. Or use a panel with a list of open files instead of tabs ("split mode").
Featherpad does have a qt dependency, which may be a dealbreaker for some.
(I am already on KDE so the QT requirement is OK)
EDIT: Tested leafpad. I will keep it around but it doesn't have tabs which I quite like to have. :)