Why did colonists want English rule to end?

Answer 1

Probably the best summary of the reasons is the list of grievances given in the Declaration of Independence. All of them are phrased in terms of what the King of England had done or failed to do although in many cases it was actually the English Parliament that was behind it:

• He has refused his Assent to Laws, the most wholesome and necessary for the public good. (if he didn't like the local laws, he declared them invalid)
• He has forbidden his Governors to pass Laws of immediate and pressing importance, unless suspended in their operation till his Assent should be obtained; and when so suspended, he has utterly neglected to attend to them. (Even the Governors he appointed were not allowed to put into force any laws they saw necessary unless they first got his approval. After declaring no local laws could take effect until he approved, them he essentially procrastinated fulfilling his duty to review and approve them)
• He has refused to pass other Laws for the accommodation of large districts of people, unless those people would relinquish the right of Representation in the Legislature, a right inestimable to them and formidable to tyrants only. (Holding hostage approval of necessary laws unless the colonists surrendered their right to representation - which most of them considered very "not cool")
• He has called together legislative bodies at places unusual, uncomfortable, and distant from the depository of their public Records, for the sole purpose of fatiguing them into compliance with his measures. (Basically trying to coerce local officials into going along with what he wanted by wearing them down physically)
• He has dissolved Representative Houses repeatedly, for opposing with manly firmness his invasions on the rights of the people. (If they criticized the English government they were simply told they were no longer allowed to have any authority and they had previously been recognized as representatives of the colonists, their recognition was revoked)
• He has refused for a long time, after such dissolutions, to cause others to be elected; whereby the Legislative powers, incapable of Annihilation, have returned to the People at large for their exercise; the State remaining in the mean time exposed to all the dangers of invasion from without, and convulsions within. (He didn't even bother to replace the local government bodies with his own - basically he left them without any government at all)
• He has endeavoured to prevent the population of these States; for that purpose obstructing the Laws for Naturalization of Foreigners; refusing to pass others to encourage their migrations hither, and raising the conditions of new Appropriations of Lands. (This one is kind of complicated but in essence he made it harder for people to immigrate here and own land - the crown was asserting that they owned all land not already owned by individuals so only the English government could grant title to land if someone wanted to acquire it - and they were making that increasingly difficult)
• He has obstructed the Administration of Justice, by refusing his Assent to Laws for establishing Judiciary powers. (He wouldn't let them set up local judges. He wanted all the judges to be his own men)
• He has made Judges dependent on his Will alone, for the tenure of their offices, and the amount and payment of their salaries. (instead of letting the colonists select their own judges - in essence the judges were political appointees )
• He has erected a multitude of New Offices, and sent hither swarms of Officers to harrass our people, and eat out their substance. (Having ousted local officials from their positions he was stocking them with his own people, who then were pretty much making the colonists pay for them to abuse the colonists - at least that's the accusation)
• He has kept among us, in times of peace, Standing Armies without the Consent of our legislatures. (The English government were sending troops to the colonies and then requiring the colonists to provide them with housing and food - at the expense of the colonists. In time of war when the troops were there to protect the colonists this might have made sense, but the accusation was that they were being forced to support troops that were only there to impose the will of the king on them)
• He has affected to render the Military independent of and superior to the Civil power. (The troops were being granted authority superior to the local constabulary and government. They were free to tell the local police and government to "take a hike" if confronted.)
• He has combined with others to subject us to a jurisdiction foreign to our constitution, and unacknowledged by our laws; giving his Assent to their Acts of pretended Legislation:
• For Quartering large bodies of armed troops among us: (as previously noted, the colonists were required to provide housing and food to sustain the troops that were there to "oppress" them)
• For protecting them, by a mock Trial, from punishment for any Murders which they should commit on the Inhabitants of these States: (the troops were not subject to local laws)
• For cutting off our Trade with all parts of the world: (the colonists were not allowed free trade - they could only engage in trade approved by the Crown. If it competed with business interests in England, they were forbidden to engage in the trade - protecting English merchants and industries at the expense of colonist merchants and industries)
• For imposing Taxes on us without our Consent: (taxation without representation since the taxes were passed in England without any representatives from the colonies)
• For depriving us in many cases, of the benefits of Trial by Jury:
• For transporting us beyond Seas to be tried for pretended offences (instead of conducting local trials under local jurisdiction)
• For abolishing the free System of English Laws in a neighbouring Province, establishing therein an Arbitrary government, and enlarging its Boundaries so as to render it at once an example and fit instrument for introducing the same absolute rule into these Colonies: (accusing them of throwing out the established rules of English law in favor of letting political appointees decide what the law was and enforce it)
• For taking away our Charters, abolishing our most valuable Laws, and altering fundamentally the Forms of our Governments: (basically overruling local governments)
• For suspending our own Legislatures, and declaring themselves invested with power to legislate for us in all cases whatsoever. (nullifying actions by local governments and dissolving them when the disagreed with the crown)
• He has abdicated Government here, by declaring us out of his Protection and waging War against us. (sort of self explanitory)
• He has plundered our seas, ravaged our Coasts, burnt our towns, and destroyed the lives of our people. (by this time the Revolutionary war was already underway)
• He is at this time transporting large Armies of foreign Mercenaries to compleat the works of death, desolation and tyranny, already begun with circumstances of Cruelty & perfidy scarcely paralleled in the most barbarous ages, and totally unworthy the Head of a civilized nation. (by this time the Revolutionary war was already underway - and yes, they were using mercenaries to fight, such as the Hessians, but in all fairness that was hardly unheard of)
• He has constrained our fellow Citizens taken Captive on the high Seas to bear Arms against their Country, to become the executioners of their friends and Brethren, or to fall themselves by their Hands. (drafting colonists against their will and forcing them to fight their fellow colonists)
• He has excited domestic insurrections amongst us, and has endeavoured to bring on the inhabitants of our frontiers, the merciless Indian Savages, whose known rule of warfare, is an undistinguished destruction of all ages, sexes and conditions. (yes - the English Government made deals with the Native Americans to fight against the colonists as part of the Revolutionary war)

Answer 2

Not all did want to rid themselves of the king. The idea that all of the colonial population was for revolution is wrong. Instead there was a large percentage who either didn't care or were still loyal to the king. At the end of the revolution 53,000 moved to New Foundland because they were loyal to the crown.

Answer 3

Whilst I agree with J Gunna, another cause of discord was that many colonists resented paying taxes to the crown in order to help Britain finance her war against France, in Europe. One popular saying that arose was: "No taxation without representation!"

Answer 4

They felt that the government was taxing them unfairly and not responsive to their needs. "No taxation without representation" was the sound bite.