(NOTE: This view was updated in the post Atheistic Agnosticism. Please read that one after this one.)
The question of whether gods and deities exist or not has been debated since humans were first able to question their reality. Everything that we could not explain was the work of some unknown force. We'd place intelligence behind anything that happened. The less we understood about it, the more intelligent something had to be to control it.
Even today, gods are used to fill in the gaps in our understanding. To this day there are still some people who believe there is a god of the sun, a god of lightning, and various demons that can possess and control you to do things you would not normally do. Humans have been around for thousands, if not millions or billions of years -- depending on who you believe and what you consider to be human -- and as recently as 1600 years ago, there were Greeks who believed every natural force of the universe had its own god powering it. There are not nearly as many gods today as there were before. Some religions even throw out all other gods and claim there is only one.
What is the correct answer? The correct answer is that we don't know. Some people claim they know but there is no evidence one way or another, none that can be claimed as scientifically verifiable. Atheists, for the most part, know that there is no current way of knowing and that is their position. We don't know, so we don't think about it. However, this position has lead people to believe we are Agnostic, and that Atheism doesn't really exist. So, I guess the question that must be answered today is:
"What is the difference between Agnosticism and Atheism?"
It's a lot simpler than some might think or lead you to believe. The difference is, in fact, fairly obvious. Let's go with the basic definition of these two terms.
One who does not hold a position.
One who does not believe in gods or deities.
Seems like a fairly strong position. There are those who consider themselves to be Agnostic Atheist or Agnostic Theist, and they are entitled to that label. However, it is not logically possible. In theory an Agnostic Atheist is one who does not believe in gods but feels they could exist. However, this is the position that the previously defined Atheist already holds.
For Atheists, the current gods that they have been made aware of do not have enough evidence to prove their existence, thus they do not believe in them. However, this does not prevent them from existing. Most Atheists will admit to believing it is possible for gods to exist. Those in the scientific community will also mostly agree that gods are not needed for the universe to exist or run. There are even those amongst Atheist who are closed minded and believe that there are no gods, never were, never will be, and nothing can change their minds. This is the worst position to take, as you simply don't know.
So, if Atheists think that there could be gods or deities, doesn't that make them Agnostic?
Not entirely. An Agnostic, as mentioned before, does not hold a position. They are confused over which side to pick. Does the Christian God exist? What about the gods of the Greeks or Romans? Maybe there are no gods... They just don't know. Imagine the gods debate as a battle field. On one side we have the Atheists and on the other we have the Theists. Agnostics are caught in the middle, stuck in the crossfire. Eventually they will be hit by one side or the other and pick a side, or they may continue to dodge the bullets and stay in the middle their entire lives. However, not picking a side is not the same as being Atheist.
So, to be truly open minded is to admit that you do not know for sure. You are basing your opinion on what you do know, but it is still just an opinion. Open minded Theists do not know if there are gods, but they believe in the one(s) they were taught. Open minded Atheists do not know if there are gods, but they don't believe in any they have been informed of.
Agnostics, just don't know.