An Etymological Approach
Since the confusion that may have sparked some of the most common misconceptions regarding atheism is most likely rooted in the frequent misuse of the terminology in daily speech, this writeup relies not on how words are used, but on what they mean.
As language evolves, the definitions of certain words change. This is inevitable, and sometimes benign. However, philosophy relies on agreement in terminology. With just a little bit of knowledge in the field of etymology, we can easily avoid this sort of confusion. Heck, you don't even have to know it by heart, just consult a dictionary with etymological notes.
In this case, the definition becomes crystal clear when looking at the origin of the words, far from popular science definitions and subdivisions into "strong" and "weak" with all the normative connotations such inventions bring about. The distinction between atheism and agnosticism becomes equally clear, and should set the most confused of minds on a straight path.
Does This Sound Like Greek to You?
If so, that's because it is. Hardly surprising, we have the wise men of Ancient Greece to thank for both of the aforementioned words. The prefix a- in both cases means not. Theos is an old Greek word meaning god (with a lower case g, as in "a god" as opposed to "the Christian God"). Hence, atheism means "not-god-ism". An atheist believes that there is not a god. In the case of agnosticism, the second part of the word comes from gnosis, knowledge, so agnosticism is the ism of "not knowledge". An agnostic believes that knowledge of the most fundamental principles of existence is unattainable. The validity of a god's existence is but one example of such knowledge, if yet a vital one.
Further Linguistic Pitfalls
The English language contributes further to the confusion in the common construction I do not believe that X is the case used to denote what should actually be stated as I believe that X is not the case. In other words, not only does an atheist not believe in the existence of a deity, but he or she believes in its nonexistence. It is not an absence of belief, but a belief in absence.
For the Record
Atheism is not the opposite of Christianity any more than Hinduism is. In fact, atheism is in no way dichotomized from religion. (The word religion stems from Latin religare, to tie down.) Buddhism is often considered an atheist religion, Buddha having a role closer to that of a saint than to that of a deity. Considering that Buddhism is all about gaining knowledge of the principles of existence, it should serve as a great example of the vast difference between atheism and agnosticism. For the sake of clarity, I state again: atheists per se do not distance themselves from religion. Most Buddhists will gladly call themselves atheists and religious.
Antinonsense
The word nontheist seems to exist only on Everything 2 (apart from some odd popular science pulp on religious belief in which the "word" was allegedly contrived) and is not recognized in any other well-known dictionary. Not surprisingly, this out-of-the-blue quasi-philosophy has been upvoted beyond belief despite a very high coefficient of BS. The definition of the prefix non- is virtually identical to that of a-, so such a word would be highly superfluous, had it existed. It does not, and on a bad day, Yours Sincerely might recommend thermonuclear therapy for the entire node. Fortunately, it is not a bad day.
This writeup is here mainly because only a minority of the writeups in this node are correct at the time of writing. A small percentage is neutral, but all too many are downright wrong, sometimes even gravely misleading. Some points covered in other writeups may be covered again here. This is mainly to clarify, to separate the information from the misinformation, and for the development of the whole argument as such.
Thanks to The Oolong Man for valued comments contributing to the well-being of Yours Truly and some minor additions to the writeup.
CentrX contributes with the following well-balanced argument:
I really don't see how anything you said means that "nontheist" is a bad word to use. While of course prevalence of usage does not equal validity, there has to be some way to make the distinction between someone who actively disbelieves in god and someone who simply lacks a belief. This is accomplished using the at least somewhat accepted terminology, like "weak atheism" or "nontheism". In your pedant conservatism in this matter, you're advocating that a new word should not be used because it obfuscated the matter, yet not having descriptive words makes it worse. Other than the etymological wrongness of the words, you provide no reason why it's "nontheism" or "weak theism" is wrong. (although in fact "nontheism" ("not god") is more active than "atheism" ("without god") etymologically, so the currently used definition of atheism should be reversed.
The Greek prefix a- means both "not" and "without", whereas the Old French/Latin non- means "not". When both words could mean "not god", the distinction is so subtle that I find this dangerous. I am not in opposition of words that can clearly show the distinction between dichotomies in belief. I simply believe that nontheist does not provide such a clear distinction, and is more likely to lead to more confusion.
Needless to say, I understand that some may disagree to this, but my personal judgment is that nontheim does not aid the language at a level required for the language to fulfil its task, namely to clearly express ideas. Therefore, until there is a clear word that is impossible to misunderstand for each branch of belief (and lack thereof), it is perhaps better to use words such as atheism, agnosticism, scepticism, and secularism in combination with any required specifications in the form of articulated reasoning rather than confusing abstractions with etymologically overlapping semantics.
I am, however, drifting off-topic. I appreciate the feedback, though.