Most of the evidence points toward Richard killing the princes (probably not personally, but having a subordinate doing the deed).
Thomas Moore’s account is a key piece of evidence. Biased or not, it told where the bodies were buried – literally. When fixing the Tower during the reign of Charles II, long after Moore wrote his account, two corpses were found in the spot that Moore’s account indicated (Moore’s account – which involved the statement of someone who was involved, indicated the corpses were thrown in a stairwell. The eyewitness said that later they were moved, but he was not present to witness that, and may only have been repeating rumor).
The two corpses were pre-pubescent children; there was no way to tell if they were male or female. The corpses were also dressed in velvet. This is important, for two reasons: Moore’s account indicated that the two boys wrapped themself in velvet robes when they were awakened and taken to be killed and, more importantly, velvet did not exist in England until the reign of Edward IV, setting the earliest possible date for the corpses. In the years from the introduction of velvet to the discovery of the corpses, only two pre-pubescent children vanished from the Tower – the two princes.
The state of the corpses also indicates Henry VII wasn’t involved. Henry didn’t become king until 1485; if Richard killed the princes, it would have been in the summer of 1483. Edward V was 12 or 13 in 1483. If he had survived Richard’s reign and had been murdered by Henry, he would have reached puberty and could have been identified as a male. (A DNA test would have proved it, but the last exhumation was in the 1930s, and there hasn’t been approval for another one to settle the issue.)
Henry had no reason to kill the princes if they lived. He did not claim the throne by right of blood; he claimed it by right of conquest. The fact that an heir might live had no relevance to his claim. In addition, Henry happened to have the rightful heir (assuming the princes were dead) in the tower when he took power. He just left the poor boy to rot in the tower (he eventually had him killed on the insistance of the king of Spain as a condition of his son Arthur marrying Catherine of Aragon, but was content otherwise to let him live).
At the same time, the princes were a major threat to Richard. He tried very hard to prove his claim via right of blood, so much so that he tried to claim that the princes were illigitimate because their father, Edward, was not legitimate. (Edward was Richard’s brother. Richard’s mother, who was still alive at the time, was not happy her son was calling her a whore, and Richard dropped the allegation).
Richard’s major opposition in the early days of his reign was the Woodville faction – friends and relatives of Edward’s widow. The Woodvilles were not royal; their sole claim to the throne was through the princes. By killing them, Richard immediately eliminated any source of opposition. (Henry didn’t count – he was just an obscure relative at the time.)
Other evidence that Richard was involved: In July of 1483, Richard stopped paying the princes’ jailer (a good sign that there would be no one alive that needed to be jailed).
Also, the Tower in the time was public grounds. People visited. And in the early weeks of the princes’ imprisonment, witnesses saw them, first exercising outside, then in the window of their cells. However, there is no account of the princes ever being seen alive later than August of 1483.
Ultimately, the evidence points very strongly in Richard’s direction. Alison Weir’s The Princes in the Tower does a masterful job of discussing the issue (she was the one who pointed out the issue with the velvet).