In Archaeology/History there is topic referred to as 'the intangible questions'. These questions appear in all ancient civilizations as well as their accounts of answers. For example, Is there a God?, Where do I go when I die?, How did we get here?, etc. Your topic falls within the category of 'intangible' or 'unanswerable' questions. However, because no definitive answer to your type of question exists the unanswerable questions are generally difused into three categories each offering its own rational.
1. mythology-its purpose is to deliever a message, devoid of time. For the ancients mythology was religion and reality one in the same
2. philosophy- requires proof...plain and simple, ancient civilizations although aware of the 'philosopher' usually ignored their philosophies caused by the 'proof' requirement. Today scientific method can be categorized this way
3. religion- faith...the only requirement is to believe
Now depending upon ones' belief system, and or perspective the topic can be answered in a number of ways, which is why it is considered a non-empirical question. However, this is not to suggest that people do not have strong viewpoints on the topic. There seems to be one constant regarding the non-empirical questions asked by humanity regardless of perspective or belief, unless one has no belief. It is the desire to know what is unknown to us. Usually relegated to faith, the fundamental need to belong to something or someone greater than ourselves suggests the idea of a higher power, presense, being, etc. It is this desire to understand where we stand in the cosmos through our attempt to answer the unanswerable questions that humanity has shown just how important those questions are to our being.
I am a fairly mediocre Christian, and have been more than skeptical about the issue of God for most of my life. However, having read the investigations of Lee Strobel into this very subject, I am convinced beyond a reasonable doubt that God, or an Intelligent Designer if you prefer, created the world. Lee Strobel was a committed athiest and investigative reporter for the Chicago Tribune who set out to learn about the mythology of Christianity after his wife became a Christian. He interviewed some of the most renowned scientists in the world, physicists, molecular biologists, etc, and at the risk of oversimplifying, the message was consistent everywhere he went: the universe is too perfect to have been created any other way. Strobel's quest into proving to his wife that Christianity was a joke ended with him becoming a Christian himself.
I will throw my hat into the ring on this one. What if we can deduce a scientific beginning to creation? This would be where Darwin or some element of Quantum Mechanics would be present. I hear many thoughts of religion and spirituality, but I think there can be a scientific position offered and thus the question is not "who" as much as "what" created the world.
I agree, we simply do not know for sure. There have been many theories put forth throughout history, but in the modern world as a whole there are basically three. There is the "it just happened" theory, for one. The second is the basis of what is usually called Hinduism and its variations, that there is a "god" which created the universe out of "himself", since "he" could not create it out of nothing. Then there is the Judeo-Christian-Islamic view, that there is a "god" which created the physical universe out of nothing, using "his" mind and will.
Interestingly, there is a reason that the latter theory refers to "god" as male. The idea is that god exists outside the physical universe, in the same sort of way that a father exists outside of the mother of their child. The child developes inside the womb of the mother, and is then born into the world, where the father lives. In the same way we are developing throughout our lives inside the physical universe, in which we live and of which we are made of the same elements. Of course the actual names of god used in the Bible give indications as to "his" nature. The first used, in the first sentence, is elohim, a female word with a plural male ending, used as a singular noun. This right off the bat shows a concept of God which transcends human concepts such as male, female, singular or plural. The word given later in Genesis as the actual personal name of God, Yahweh (or Jehovah, spelled yod-he-vau-he in Hebrew) means "I am that I am," a continuing form of the verb "to be."
But to get back to the question at hand, yeah, we really don't know. There is nothing about the purely scientific view that cannot be fit into one of the other two theories. The Big Bang can as easily be Vishnu's dream as a purely physical creation of energy, as easily a cosmic explosion as "Let there be light." When you realize that the word translated in the King James Bible as "day" in the first chapter is not the Hebrew word for "day" but a term meaning "cycle of time" with no restriction on how short or long the cycle may be, it sort of negates the seven 24-hour day idea. There's a possibility that we may never actually know for certain what the causative agent (if any) was.
I'll sort of support grouchygirl's answer --- but a bit more directly. We just don't know. And, of course, the choice of the "who" pronoun would indicate an operative in some way "humanoid." This is the way we generally think of God --- as a spirit that appears to be a human. We often refer to God as a "he" although there is not reason why God could not be a "she" --- basically because, if God is a spirit, he/she is neither.
You may elect to believe, as does sloand92, that the account of creation in the Bible is "correct," but it is only one of many, and may never have been intended to provide a scientific explanation, only a moral one showing us that creation is not the result of some random act. Since the world was created with meaning and intent, it/we must have purpose.
But back to the question --- we just don't know; we may believe many things, but we just don't know.
The answer depends on your culture and belief system.
Scientifically speaking, our world was created when a planet, or star, exploded and the pieces fell into orbit around our current sun. Through thousands of years of evolution and climate changes, man finally surfaced and has been evolving since.
If you are of the Christian/Jewish/Muslim faith however, then the world was created by God (also known in the scriptures as Yahweh) and after a short time he created man, and woman, as his children and in his image.
If you reach further back than that - the Greeks believed the world was created by Chaos who gave birth to Gaea (earth) and she gives birth to Uranus (sky). Their children (the Titans and cyclops) begin a war that Zeus wins and he sends a flood to destroy the world with only one woman and man (Gaea and Uranus) surviving. When the floods end, Gaea and Uranus throw stones over their shoulders and create man.
There is also the Norse version which cites Niflheim as giving rise to 12 rivers which eventually produce Ymir, a giant cow, that licks a stone and creates man. This man, Bor, has three sons and they go on to create man out of tree logs.
And then there is the Hopi Native American version which has the creator, Taiowa, instructing his nephew Sotuknang, to establish nine universes (pretty interesting if you think up until recently there were 9 planets in the solar system and the Native Americans were big into the sky and the stars). Sotuknang creates Spider Woman who creates everything ,including man, from there.
Which one is the true creation story? It's not that black and white. Although science lays claim to it being the most factual, it can't explain everything and that's what creation stories are trying to accomplish. They aren't merely explaining how the mountains came to be or how man came to be, they are explaining how human traits came to be; good, evil, pain and suffering. As for who created the world..it's a lot like the question 'How many licks does it take to get to the tootsie roll center of the Tootsie Pop?' The world may never know.