Haaretz reports the Central Statistics Bureau finding that 44% of the Jews in Israel define themselves as 'secular.' I am sure that's accurate. It is also deceptive in extremis. The word 'secular' (חילוני) bears two distinct meanings in contemporary parlance. 1) Ideologically secular, axiologically cosmopolitan and (usually) anti-Orthodox in some way 2) Non-Orthodox (for whatever reason), but interested in having a distinct, Jewish element in their lives.
According to the Guttmann Study, this 44% subdivides into 10-15% that belong to Group no. 1 and around 30% belonging to Group no. 2. In other words, as I've noted before, the important figures (as Israel struggles with its identity) are that fully 85% of the Jewish population want a distinctively Jewish State, while only 15% (a very vocal, media/academic/influential minority) want a cosmopolitan 'State of all its Citizens.'
Other studies back up this finding (despite the wishful thinking of the Haaretz staff and its Cafe pseudo-Intellectuals). Israelis overwhelmingly define themselves as Jews first and Israelis second. Israelis overwhelmingly believe in God. 99% of Israelis circumcise their children. 99% put mezuzot on their door(s). 95% attend a Seder (of some sort). 75% fast on Yom Kippur (and the 25% includes those too ill to fast). [On an anecdotal note, I wish I had NIS10 for every secular student who told me that they have come to respect and identify with Judaism, and that it's the rabbinate that turns them off.]