Why were the American colonies unhappy with the British government?

The American colonists had a number of grievances against the British government, although they were all related in some way to the issue of autonomy, or the ability of Americans to run their own affairs. Most colonists were committed to the connection between America and Great Britain, but still valued a certain degree of independence in the day-to-day running of their affairs. Over time, British policy on America contributed to a growing sense among the colonists that they were not being respected or treated fairly by the mother country in a number of key areas.
The catalyst for much of the colonists' dissatisfaction was the French and Indian War. Having prevailed in the conflict, the British felt that it was necessary for them to keep their troops stationed on American soil. For the most part, the colonists were strongly against this measure, not least because they'd have to pay for it. At that time, standing or permanent armies were quite rare. Soldiers tended to be recruited on an ad hoc basis, only called up when there was a war to be fought. Once the ensuing conflict was over, they would be demobilized until they were needed again. Having a permanent army, however, was seen as dangerous, as it could so easily be used by the authorities as an instrument of repression, and that was what the American colonists feared.
As a result of the recent war, the British had incurred substantial debts and so needed to find a way to pay them off. Once again, they looked to the American colonists to make up the shortfall. Legislation such as the notorious Stamp Act of 1765 and the Townsend Acts of 1767 was deeply unpopular as it placed an excessive burden of taxation on the colonists. Worse still, from the American point of view, was the fact that they had no influence over these laws due to their lack of political representation in the Westminster parliament.
Under such conditions, it's not surprising that colonists resorted to more direct methods of action such as the famous Boston Tea Party, where chests of imported tea were dumped in Boston harbor in protest against the imposition of tea duty. As a direct result of the disturbances, the British government passed the draconian Coercive Acts in 1774, which drove the two sides further apart and brought the prospect of armed conflict ever closer.