Edit:
I do realize that there are some newer Nationalist parties like Geert Wilder's Party and the Swedish Democrats who seem to be mildly pro-Israel, but they are newer parties and seem to be more anti-Muslim due to immigration than pro-Israel. Many of the older, more traditional conservative parties like Front National in France have roots in antisemitism. Then there are the other traditional right-wing parties like Jobbik and Golden Dawn which are very antisemitic.
Meanwhile, Republicans in the USA are incredibly pro-Israel. I've never seen a modern Republican in the US say anything supportive of Palestine. However, I've seen pictures in the 1960's of segregationists blaming Jews for integration, communism, and the Civil Rights Act. So what changed for them?
Part of it is undoubtedly the question of religion. Zionists have historically been supported by evangelical Christians in the United States very fervently, and the fact that they typically line up with the right-wing (or at least, have usually in the time Israel has been around as a nation-state) means that the right-wing already has one bloc in favor of Israel. Charles D. Smith writes in Palestine and the Arab Israeli Conflict, some evangelical Christians held the belief from very early on in the Zionist movement that bringing the Jews back to the Holy Land and creating a state of their own there, along with converting them then to Christianity, would help them when the Day of Judgment (which they believed was close at hand) came around. This trend appears to have continued for quite some time, resulting in evangelical support which continued to be more prominent as Republican presidents took office more often after FDR and Truman, and as they relied more on the growing evangelical base. As a quick note, the proportion of those identifying themselves as having a "born again" experience, or being "born again" Christians has gone up over time, even slightly, and their support as a bloc has seemingly become more unified and important, but this is mainly due to their high voter turnout. As noted in the article "Evangelicals in the Post-Reagan Era: An Analysis of Evangelical Voters in the 1988 Presidential Election":
First, there has been an important shift in the partisan identification of white evangelical voters during the past decade. A shift toward Republican identification took place during the early 1980s, and this shift appears to have solidified during Reagan's second term...Second,it would appear that white evangelicals have become more politicized during the past decade.
This mobilization among evangelical Christians helped solidify the right's support for Israel in the United States. It also draws greatly from other factors which are much, much harder to pin down.
Support for Israel wasn't something that originated with Republicans, necessarily. In fact, President Johnson is often considered to be the person who began the alliance with Israel, after Kennedy's deal to sell Israel Hawk missiles (first direct arms), the first military loans to Israel in 1962, and the increase in aid to Israel by 450% in 1968. The approval under Johnson to sell Israel Phantom fighter bombers is where many mark the alliance to really begin, and Johnson was a Democrat.
The support for Israel has also traditionally been very strong, and while right-wingers were more likely to be in favor of it, it's still been fairly common across party lines. Though Republicans are typically most staunch in support, overall sympathies have reached as high as the noted 64% in the early 90s. Much of this support came as a result of the anti-Soviet doctrine: Israel, after 1967, was seen as the only nation the United States could influence and keep away from the Soviet sphere of influence decisively, as the Soviets eagerly made arms deals with the Arab states (Egyptians, Syrians, etc.) around Israel. Israel would later be used as a sort of "springboard" to solidify relations with Israel through the Camp David Accords, which signalled the start of an American-Egyptian alliance.
Israel's ability to stay anti-Soviet, coupled with the growing evangelical movement in the '80s, and the end of the First Intifada along with the Oslo Accords, signalled the early 1990s support that I mentioned among Americans.
As for Europe, I'm somewhat tired and don't think I have the books I need to answer that portion on me, so hopefully someone can expand on that side. But with the United States, the right-wing has typically supported Israel more because of the evangelical base, the strategic value against the Soviet Union, and the general American support it affords them. Conservatives are typically "realists" in international theory, and view the world as a lot more dangerous than "liberal" international theorists, and so they hope to choose stable, powerful allies (Israel's military might was fairly well established even before US aid, thanks to the 1967 war, though 1973 was a severe test thereof) to offset the power of other alliances (like, say, the Soviet-Arab alliances).
It's a complicated thing to discuss, hopefully someone can do the comparison to Europe and explain that end a little. Even what I've said is probably only the tip of the iceberg :).
Greetings everyone. In the few minutes this sub has been up, it's attracting sub-standard responses. Just a reminder of a few of the rules:
no responses covering events/conditions post-1994, per this sub's "20-year rule" prohibiting discussion of current events
no anecdotes
no speculation
OP: your question implies that you're asking about both current policy and historical reasons. If you want to pursue discussion on the former, do consider x-posting that question to another sub, e.g. /r/politics
I can tell you a little but about western Europe's relationship with Israel in the early years of the State of Israel (though it is important to note that some European nations have strong ties to Israel in the modern era - they simply lack the resources to support Israel in the way America does/Israel has no need for their technical and military support in the way that it has America's).
It is worth noting that in 1952 Konrad Adenauer, the conservative Chancellor of Germany, agreed a reparations treaty with Israel agreeing to pay DM 100 billion to the state of Israel as restitution to those Jews who had perished in the holocaust/had their property confiscated who had no surviving relatives. This was a big political risk for Adenauer, as in Germany just 5% of west Germans admitted feeling "guilty" towards the Jews, and also for the Israeli government - many Israelis and jews felt very strongly that accepting reparations was tantamount to forgiveness for Nazi crimes, which many were not prepared to give in any circumstances. However the treaty went ahead, which gave Germany a big hand in the early finances of the State of Israel - reparations were as much as 87.5% of the state's income in 1956.
Britain and France had a somewhat close relationship with Israel in the 1950s and 1960s. Britain's relationship with Israel got off to a slightly more shaky start as it was Britain that had been in control of Palestine from WWI onwards - Britain had unceremoniously pulled out of Palestine having been unable to combat the rising tensions and attacks by Palestinian and Jewish right-wing groups (see e.g http://en.wikipedia.org/wiki/King_David_Hotel_bombing). Britain's support for Israel had often been mixed, owing to Britain's longstanding interests in the region. Britain was often seen as pro-Arab, and did not want to risk losing support in a region in which for much of the period between the 1940s and 1970s, perhaps even on to the 1980s, it still saw itself as a major player.
France however, despite similar interests in North Africa, Lebanon and Syria, had a closer relationship with Israel from the start - it is worth noting that France, and its North African possessions, had Europe's largest Jewish population post-WWII, so may have been more culturally inclined to cooperate with Israel. In the 1950s France began selling weapons to the IDF, such as Dassault Mirage fighter jets. There have been suggestions that it was France that gave Israel the help it needed to begin its nuclear programme.
However both nations saw the peak of their cooperation with Israel during the Suez Crisis, precipitated by Arab Nationalist/Socialist Gamal Abdul Nasser's siezing of power in Egypt and nationalization of the Suez Canal, which had been owned by the Suez Canal Company. Egypt, whilst it had been nominally independent since the 1920s, had been heavily controlled by Britain, for whom the Suez Canal was an important lifeline to its possessions in the east. The Canal was similarly important to France. Meanwhile Arab-Israeli tensions had resulted in Egypt's blockade of the Gulf of Aqaba, which the Israeli government was determined to put an end to.
In 1956 Israel, France and Britain hatched a secret plan (ignoring a 1950 treaty that committed France, Britain and America to work together in the event of any threat to the state of Israel) to conduct joint military operations in order for Israel to occupy the Sinai peninsula and Britain and France to occupy the Suez Canal Zone. They were militarily successful, but American and international pressure forced Britain and France to withdraw from the Suez Canal Zone.
Tony Judt posits that the whole affair had a profound impact on all four countries:
Israelis saw that whatever their reliance on French military hardware, their best bet for survival in the long term was to tie themselves to the world's new hegemon, the United States, and align theirs and Washington's interests as closely as possible.
Suez reminded the United States of its new responsibilities in the post-WWII world. Eisenhower was angry that Eden (the British PM) and Mollet (the French PM) had simply assumed that the United States would tacitly support their aggression against Egypt.
Even more so, America was angry they had unwittingly handed a propaganda victory to the USSR; it was at exactly this time that the Soviet Union sent tanks to Hungary to suppress a nascent movement to free Hungary from Moscow's shackles and run the country on more democratic lines. This was hidden in most of the world by news of France and Britain's naked imperialist ambitions in the Middle East, and the Soviet Union (which had no real intention of intervening) was able to play protector by handing a diplomatic note to the west demanding British and French withdrawal. The Middle East would come to play a key role in America's anti-Soviet policies, with the US declaring in 1957 that it would oppose all "International Communist" aggression in the Middle East; Israel would be a key partner in resisting Soviet incursions in the Middle East.
It was on Britain that the effects fell hardest - there could be no clearer demonstration that Britain no longer had the resources to back up a global empire. American economic pressure during the crisis had decimated Britain's foreign exchange reserves and risked a run on the pound; Britain could no longer afford to be at the top table alone. Britain had been marginalised and it was from this point on that British colonies would be handed independence at a growing pace, a global retreat which culminated in the withdrawal of all British troops, ports and bases "East of Suez" in 1971. Secondly the UK establishment realised that "must never again find itself on the wrong side of an argument with Washington", leading to the very close international cooperation of London and Washington for decades to come.
France (and future President de Gaulle in particular) drew the exact opposite conclusion from the USA's display of willingness to rebuke its allies - France must maintain its ability to act independently and not rely on the support of its allies. It was this course that would lead to France beginning to withdraw its fleets from NATO control in 1958 and ordering that no foreign nuclear weapons be stationed on its soil. The French military wanted to ensure that, in the event of an invasion from East Germany, they would be able to fight independently from the west and reach a separate peace if necessary.
I have ventured somewhat off topic here, but I hope it demonstrates a point - the close relationship of America and Israel is not just a function of internal American politics (although the relationship between Israel, America's Jews, America's left, and then the American right and American evangelists, explains how it was possible), but also represents the story of America's unparalleled global reach and power in the post-WWII world.
Whether western Europe wanted to be Israel's ally and protector in the Middle East after 1948, both they and Israel came to realise that only America could play that role. The goings on the in the Middle East in the 1950s arguably helped set the future course for Europe's two former imperial powers.
Sources: Mostly Postwar by Tony Judt.