Albus Dumbledore trusts Severus Snape. Let us not presume that the foundation of this trust is based merely the fact that Snape begged for it, pleading that he is now innocent. Dumbledore, not only the greatest, most intelligent wizard alive, was also a member of the Wizengamot, and was already immune to such pleas from numerous Death Eaters claiming they are reformed in their ways, especially after the fall of Voldemort. Snape must have performed other deeds to warrant his relationship with Dumbledore, which will hopefully be spoken of Book Seven. These deeds were, obivously, either genuine or a ploy masterminded by Snape and Voldemort to fool Dumbledore. However, trickery is one thing, let alone creating an illusion upon the most intellectually gifted man alive that one of the most loyal servants of his greatest enemy has become a powerful ally is another. (That is, of course, without the use of Polyjuice Potion or any other disguising measures.)
So now that we have established that Snape is probably on the side of Dumbledore, let us theorize as to why he murdered him. (Before we begin, however, I would like to note that all comments I make in the following paragraphs are made as if Snape is in fact against Voldemort.)
Firstly, let us begin with the Unbreakable Vow. I believe Voldemort had already asked Snape that, should Draco fail to kill Dumbledore, Snape would perform the task himself. Snape, not wanting to blow his cover, agreed to it. However, when the time came to murder Dumbledore, that is when Snape would show his true allegiance and refuse to do it,and probably be killed by Voldemort for his betrayal. Better than being murdered on the spot for refusing Voldemort's wishes. This way, he can continue to spy for another year. Since he had already promised Voldemort that he would kill Dumbledore, denying to Narcissa Malfoy that he'd do it would blow his cover as well, even if it were in an Unbreakable Vow. Snape had already accepted his death to come soon.
Next, let us move on the conversation between Draco and Snape overheard by Harry. When Harry reported this to Dumbledore, Dumbledore become aware of the vow. He knew that either he or Snape must die. Valuing the life of a spy who could help Harry through the inside more than his own life, Dumbledore ordered that Snape should murder him to save himself. However, Snape was not so easy to convince, as he is loyal to Dumbledore and would rather sacrifice himself for Dumbledore. This is what they were arguing about when Hagrid overheard. Snape refused to assassinate his true master.
Finally, we reach the actual murder. After Snape entered, Dumbledore pleaded with him. Why would Dumbledore plead? Even if he were about to die, that is below him. Plus, Dumbledore has his defenses even without a wand. Fawkes, for instance, would have come to his help had he wanted it. Dumbledore, a small, agile man, could have attempted to dodge the curse. Weak as he was, when one is endangered, they suddenly become stronger, faster. Harry has blown up his aunt without a wand. Why couldn't the greatest wizard of all time do something similiar, especially when he was one-on-one with Draco, a small boy? No, Dumbledore pleaded not for his life to be spared, but instead that his life be sacrificed. This is why Snape appeared revolted. He has no reason to hate a man who has saved him from Azkaban, given him a job when all others thought him evil. He only has reason to hate having to kill that man.
After the murder, had Snape been evil, he would have taken Harry to Voldemort with him to finish him off. Snape did not even fight back against Harry. Snape has never attempted to hurt Harry or Dumbledore before, not even if Book Five when Voldemort had returned, and did not attempt to hurt anyone else even after people believed him to be evil in Book Six.
This is why I believe the murder of Albus Dumbledore by Severus Snape was planned and masterminded by the victim himself.