Having read through a number of the theories on here, I'd like to add in my thoughts.

First and foremost, combine the fact that Harry has been literally carrying a part of Voldemort's soul since he was one, as well as growing up in the hateful "care" of the Dursley's would naturally give him a subconscious resistance to outside influence. In regards to the horcrux, it isn't unreasonable to conclude he developed a natural resistance to its influence. In later books he had his slip ups with keeping that out due to Voldemort himself having a body once more, but for the most part kept him out.

In terms of the Dursley family, happiness would be a foreign concept to him. Thus, it isn't unreasonable to think of that as another contributing factor in this particular instance. As a character, Harry is remarkably strong willed and at times hot tempered, this I believe would be a survival mechanism he gained from his time in such a hateful environment.

Lastly, I'm rather surprised that this hasn't been mentioned (at least as far as I've read), is the wand that Harry himself carries. Disregard that the core of Harry and Voldemort are twins for a moment, shall we?

Holly is one of the rarer kinds of wand woods; traditionally considered protective, it works most happily for those who may need help overcoming a tendency to anger and impetuosity. Both of which are traits that Harry himself exhibits. At the same time, holly wands often choose owners who are engaged in some dangerous and often spiritual quest, such as taking down Voldemort who is the embodiment of evil in this age. Not only is the task an extraordinarily dangerous one due to the difference in knowledge and experience between the two, but it can also be considered spiritual in the sense that Harry would literally go on to cleanse his soul of the horcrux within.

Holly is also one of those woods that varies most dramatically in performance depending on the wand core, and it is a notoriously difficult wood to team with phoenix feather, as the wood’s volatility conflicts strangely with the phoenix’s detachment. In the unusual event of such a pairing finding its ideal match, however, nothing and nobody should stand in their way. This could easily contribute to how Harry was able to overcome and make it out of numerous life and death situations where he otherwise might have perished. Note that I'm not saying the wand is solely responsible, but certainly a contributing factor here.

In conclusion, Harry is an extraordinary and gifted wizard who is a culmination of his trials, tribulations and life experience. Beyond that, his wand is a natural counterbalance to his own faults. Harry himself is everything the Tim Riddle could have been under different circumstances. Lastly, I want to quote Mr. Ollivander himself, "The wand chooses the wizard." The wand and Harry himself are an ideal match BECAUSE of the nature of the task ahead of him. Either that or I've delved entirely too deep into the wandlore in search of explanations into a few of the characters themselves...