New Game +

For those of you who have played games, mostly RPGs, like Chrono Trigger or The World Ends With You, you'll understand what New Game + is. For those who haven't, it's essentially taking all of your stats, weapons, etc from the end of the game and starting all over at the beginning at your end game level. Do you think this should be in more games or does it take the fun/challenge factor away? And I don't just mean RPGs, but other genres as well?