My lines appear everywhere, even on the Wii menu. The lines are in different places depending on what the Wii is doing. For example on the News Channels they are more collected toward the center of the screen. I haven't played any games since there are none worth playing, but I imagine they show up in games as well. Regardless, Nintendo offered to replace the Wii outright, but I said I'd rather try and keep what is saved in the backup RAM since I have 99 Miis in there. So I have to send my Wii to Nintendo (they pay shipping).
Black Tiger, your problem will likely get worse. Be sure to send it in before a year is up!