For anyone who is interested in Jewish history, biblical archeaology, or art, this is a must see. A lot of the artifacts and things that have been discovered throughout Israel are housed here. (Occasionally, you will see reproductions at the site that it was found, but the originals are here.)
The oldest piece of Scripture is here, as well as the Dead Sea Scrolls. Many people come just to see the scrolls and it is worth it. The Dead Sea Scrolls are a fascinating story and here you are able to see the entire scroll of Isiah, which I believe was found almost in its entirety.
While I was there, there was a display on the Jewish people of Yemen and it was fascinating to see the differences in culture and the various artifacts they had perserved there.