How frequently does the USA veto anti-Israeli UN Security Council resolutions?
The Security Council is the only international body whose decisions are genuinely "law" and need to be obeyed. That is because they imply an agreement between the world's great powers: USA, Russia, China the UK and France and can be implemented by force (though that requires a further decision). To give you an example, if the International Court in the Hague makes a decision, it becomes a recommendation to the Security Council. If the council ignores it or it is vetoed it has little or no significance. The same applies to UN General Assembly votes: they are recommendations to the Security Council and can be ignored or vetoed. The "big five" members basically take all the decisions and a great power consensus is required for any action to be taken.
There are 10 temporary Security Council members drawn from the General Assembly on a mixed rota-election system. Those members can make proposals for the others to veto or forget. This is significant because about 15% of UN states are Arab and a further 15% Moslem, so they are almost always in the Security Council. Israel has never sat on the Security Council and as the only "Jewish" state is clearly very isolated at the UN. At present Jordan is the only Arab member and Nigeria the only largely Moslem country in the Security Council so Israel has a relatively easy period.
So how often does the USA veto anti-Israel decisions?
I counted vetoes from the UN's foundation to 2009. In total 185 vetoes were cast in that period, of which 96 were cast by the USSR/Russia (mainly the USSR) and 78 by the USA. In some cases the other permanent members participated in vetoes, mainly the UK voting with the USA but also France and China occasionally cast vetoes.
The USA did not cast a single veto before 1970. Most of the USSR's vetoes were cast in that period when the UN and the Security Council were dominated by pro-Western states. Following decolonization, the emergence of a third world voting block shifted power to the Soviet block and the USA then cast lot of vetoes, primarily in reference to the Middle East and Vietnam war.
In the 23 year period 1946-1969, when the USA cast no vetoes at all, the USSR cast 80 vetoes of which 5 vetoes related to Israel: the causes were Syrian-Israeli conflict over water diversions, Egyptian-Israeli conflict over access to the Red Sea and attacks on Israeli civilians.
From 1970 to 2009 the USSR/Russia cast 16 vetoes, only one of which related to the Middle East: In 1984 the USSR rejected a call for withdrawal of all foreign forces from Lebanon, then occupied by Syria and Israel. Since 2010 it has cast a number of vetoes related to Syria.
France and the UK cast 8 vetoes in the 1946-1969 period. All with relation to the decolonization of Africa, two were about the Sinai crisis.
In the 30 year period 1970-2009, the USA cast 78 vetoes of which 39 - exactly half- were related to the Middle East, so on average the USA has vetoed one anti-Israeli decision a year since 1970.
Democrats governed the USA in 1977-1980, 1993-2000, 12 years out of the 40 year period examined: Only 6 vetoes were cast by Democratic presidents, but 4 of those were Israel-related (one or two per presidential term).
Half of all US Security Council vetoes were during the Reagan presidency, and it also was responsible for half of all Israel-related vetoes, either in relation to the occupied territories or the Israeli invasion of Lebanon. 10 vetoes were cast during the presidency of George Bush Junior of which only one was not related to Israel, in other words 3/4 of all pro-Israeli vetoes were cast by two US presidents.
The necessity of using the veto is often the product of poor inter-state relations. The point about the security council is that issues are resolved in back rooms and not through global confrontation. Use of vetoes are a form of low level confrontation and the high incidence of vetoes under Reagan and Bush may reflect poor inter-state relations, with Israel being an easy way to embarrass the USA because of its lack of international support.
Because I only studied vetoes I can't comment on what the Security Council was actually deciding, and strictly speaking the two need to be examined side by side. Israel is not the only long-term conflict, though it is arguably the UN's oldest conflict. India-Pakistan, Sri-Lanka, Tibet, Sudan and Congo all come to mind and they attracted almost no vetoes.
So is Israel dependent on the US veto? I would say, yes, but less then once a year.
Source: United Nations Security Council - Veto List