Who is the leader of the State of Israel?

Answer 1

Israel is a democracy,

The President is the "leader" of Israel (Head of State) but he doesn't have rights to control Israel and he is just symbol of Israel, the Prime Minister is the one who lead Israel (Head of Government).

The current (Dec 2013) Prime Minister of the State of Israel is Benjamin Netanyahu.

The Prime Minister is the leader of the political party that wins the greatest number of Knesset (parliament) seats in a general election. The primary political power lies in the office of Prime Minister. Currently, the Likkud conservative political party, has the most seats in the Knesset.

The current (Dec 2013) President of the State of Israel is Shimon Peres. While the Presidency in Israel is largely a ceremonial role, given Peres's long career in public service, he has more political influence than Israeli presidents typically have. The President is elected by the Knesset, to serve a term of seven years, and cannot be re-elected to the position of President.
The President of Israel only serves as a ceremonial figurehead while the Prime Minister holds the power of the Executive branch. As of 2014, Benjamin Netanyahu is Israel's leader.

Answer 2

It depends on what you are calling "Palestine".

If you are referring to the Palestinian Authority, which has de jure authority over both the West Bank and the Gaza Strip, but has only de facto authority in certain parts of the West Bank, the current leader is Mahmood Abbas (affectionately nicknamed Abu Mazen).

If you are referring to the Gaza Strip, Hamas exerts de facto control in that territory and has Ismail Haniyeh as it ruler in that territory.

Answer 3

Just as in Canada, England, Australia, South Africa, Japan, and countless other
representative democracies around the world, the political leader and head of
state of Israel is the Prime Minister.