The State of Israel has begun the process of publishing its collection online. You can visit the site at http://www.archives.gov.il. This is no small task, as the archive houses more than 400 million documents, video and audio clips, many of them classified. The archive was established in 1949.
The archives do not currently have an English-language interface, but Google translate helps.
I went to the website and immediately had a good find – my grandfather’s passport, featuring a beautiful photo of him with my Nana.