The ARCHINET initiative launched during September.
From the NLI Web Site:
The Israeli Internet Archive is intended to preserve online publications published on Israeli websites for coming generations, just as books and other printed material are preserved.
In recent years the internet has become a central arena for Israeli culture, a place where a large number of written and visual materials are published. The materials that are published in the virtual world are an important part of the cultural life of the State of Israel and Israeli public discourse, and it is the library’s duty to be concerned with their preservation for researchers, students and all those who are interested- today and in the future.
At this stage, the National Library will copy and preserve Israeli websites that are listed under the ending *.il.
From the ARCHINET FAQ:
How can I view the Israeli Internet Archive?
For reasons related to copyright law, at this stage, it will only be possible to view the archive in the building of the National Library. The materials in the archive will be included in “Merhav”, the unified search function of the National Library, such that in a search done in the “Merhav” system from the Library’s building will include pages from the archive.
How often will the archive be updated?
The websites will be scanned and copied about twice a year.
Read the Complete FAQ
UPDATE October 7, 2013 Preserving the Web: National library to archive almost all Israeli websites (via Haaretz, Fee-Based)
Note: You can read the full text article without an online sub to the newspaper via the Google cache.