I'm about to get one for Legend of Zelda: Skyward Sword, but I'm wondering if it will make any difference to games that don't need it, like Legend of Zelda: Twilight Princess?
No, games that are not specifically designed to use the Wii Motion Plus will not recognize the technology and will benefit from no advantage whatsoever. Only games designed for it can use it.
You can, however, play non-Motion Plus games with the Motion Plus attached to your Wiimote or with the WiimotePlus with no adverse effect.
Taken from Wikipedia: