If anything, the Suez crisis was a unifying moment for Egypt. You might be able to say that President Nasser of Egypt was able to become more dictatorial as a result, but he was already a dictator so that wasn't really much of a change. Also, you're forgetting one other participant: Israel. Israel got exactly what it wanted - a secure southern border and the reopening of the straits of Tiran.

It was the UK and France who came out of it destabilised. The Suez crisis accelerated the collapse of the British and French colonial empires. In particular, it's often said to mark the date that Britain ceased to be a superpower.

As for why the UK wanted control of the canal: the UK owned the canal until Nasser decided to seize it. The UK bought it legally from the Khedive of Egypt shortly after it was built in the 1870s. When Nasser seized it it was a serious blow to British pride. Moreover, Britain still had colonies in Asia, which made the canal a strategic necessity. France's motivation was to make sure middle eastern oil continued to flow through the canal uninterrupted, and also to take Nasser down a peg. Nasser was an Arab nationalist, and his ideology (and willingness to arm groups who shared it) was a threat to France's north African colonies. There's also the fact that Nasser was a nationalist dictator shortly after WW2 - after their experience with appeasing Germany in the 1930s, Britain and France were perhaps a little over-eager not to repeat that mistake. Anthony Eden, the British Prime Minister, referred to Nasser as a little Hitler.

The long term repercussions:

- Deepening of the tensions between Israel and the Arab world.

It's hard to know how much of a difference this made, since things were already pretty tense, but Israel's attack on Egypt and the subsequent lack of a clear peace settlement between them definitely didn't help.

- Emboldening Nasser and his Arab nationalism.

Again, it's hard to know how much of a difference this made since Nasser was already a dictator, but it's definitely possible that it increased the likelihood of another clash with Israel.

It's possible that without Suez, tensions would never have got bad enough between Israel and Egypt to lead to another war, and the borders of Israel and Palestine would have remained as they were in the 1950s. So no Israeli occupation of the West Bank and Gaza. This is purely speculation though. Either way, it's unlikely that Israel would have ever normalised its relations with its Arab neighbours.

- The disintegration of the British and French empires.

Suez was a huge embarrassment for both parties. France didn't want to give up its empire, but the loss of prestige dealt a serious blow to their efforts to convince their African colonies to remain loyal to France. In Britain, the Suez Crisis toppled the government, and led to a political push towards faster decolonisation. The speed at which decolonisation progressed from then on could very well be a major factor in why so much of Africa failed to form stable governments.

- Severe damage to the relationship between the USA and its European allies.

Needless to say, America threatening to crash the British and French economies unless they bowed to America's demands didn't go down well. This led France to develop its own nuclear deterrent, break away from NATO entirely in 1966. It also strained America's relationship with West Germany, as by backing Egypt America was essentially siding with the Soviet Union against its European allies. The Soviets had threatened to nuke Britain and France if they didn't withdraw from Suez. The fact that the Americans had responded to a threat to nuke Europe by agreeing with the Soviets called the whole alliance into question. It may well have influenced the development of the European Union.

- Reduction of British involvement in the Middle East, and greater American involvement

Before Suez, Britain had been the main power-broker in the middle east. Afterwards, America got more involved. Ironically in siding with Egypt America only made itself less popular with the Arabs, as any intervention was seen as colonialism.

- Emboldening Kruschchev and Soviet nuclear policy.

The fact that after the USSR's nuclear threat Britain and France had backed down, and America had done nothing, convinced Kruschchev that this was a good strategy (never mind the fact that it was the American threat of economic intervention that had forced Britain and France to withdraw). This may well have directly led to the Cuban missile crisis.