Which ideas most influenced the founding fathers of the USA?

The Founding Fathers were the intelligent men who were able to draft the constitution that has endured for the last few centuries. The ideas that influenced them have equally endured.

First and foremost, they were religious men and saw religious freedom as a fundamental basis for a functioning society. Though they didn't believe in a God-given right to rule (as was the case with the English monarchy of the time), they believed all men were created equal before God and accordingly, rights were given. As it is stated in the Virginia Bill of Rights, Article 16 dated June 12, 1776,

[R]eligion, or the duty which we owe our creator, and the manner of discharging it, can be directed only by reason and conviction, not by force or violence; and therefore all men are equally entitled to the free exercise of religion, according to the dictates of conscience; and this is the mutual duty of all to practice Christian forbearance, love, and charity towards each other.

Note that the last part of the quote mentioning that all should practice Christian values means exactly that. It does not call for all to be Christians. Rather, the Founding Fathers called for a moral that could be found under the Christian heading.

The works that greatly influenced the Founding Fathers in their enterprise include John Locke's philosophical writings. His social contract in particular was of great use – ideas on property, where money came from and its moral use, and where possessing firearms to defend and possibly overthrow an unrighteous government is acceptable and necessary. (The relevant works include “Two treatise of Government” - arguably the most influential -, “An Essay Concerning Human Understanding”, “Reasonableness of Christianity”, and “Letter Concerning Toleration” among others.)

Another key document which influenced the Founding Fathers is the Magna Carta (its rightful name being Magna Carta Libertatum). The Magna Carta was a charter which was agreed to in 1215 by King John of England and a band of rebel barons. It guaranteed protection of church rights, illegal imprisonment of said barons, access to rapid justice, and allowed for a reduced and limited feudal payment to the Crown. The Magna Carta eventually served as the basis for English common law and became a symbol of freedom from oppression to Englishmen – including the Founding Fathers who found inspiration in it.

There are other authors and works that influenced the Founding Fathers such as the Bible, Montesquieu, Sir William Blackstone, and David Hume.

The first link gives good historical background and references at the end other documents that were influential.

This second link emphasizes the religious background and education of the Founding Fathers.