I don't use Ai very often. I created a line art graphic in Ai, saved it and saved a copy as .eps. It looks beautiful in Ai but when I place it into ID all the lines are jagged/blurred. I tried copying it into PS and saving as a TIFF but that was worse. What am I doing wrong?

Save as an AI and import it as an ai file into ID, then make certain you have high performance for the display option.

No need to save as an eps but if you want also choose High Performance as the display option.