Agnostic theism is belief in God without the claim to know. It has a long religious pedigree rather than being a modern hedge: a great deal of theology insists that God exceeds human knowledge, and faith in most traditions is distinguished from certainty rather than identified with it. The believer who acknowledges doubt is a familiar rather than an anomalous figure.
Agnostic atheism is the absence of belief without the claim to know that there is no God. This is how a large proportion of modern unbelief describes itself when pressed, and it is the position that generates the recurring argument about where the burden of proof lies.
Ignosticism, also called theological noncognitivism, holds that the question is not well formed until "God" has been given a coherent definition, and that the competing definitions are so various that no single question is being asked at all. It has roots in logical positivism and in A. J. Ayer's verificationism, though it does not depend on them, and it is often expressed as the demand that one be told what is being asserted before being asked whether one believes it.
Apatheism is indifference to the question, the view that whether God exists makes no practical difference and does not warrant the attention. It is a stance rather than a doctrine, and survey researchers increasingly identify it as the actual position of much of the growing religiously unaffiliated population, whose members are more often uninterested than opposed.
Antitheism is active opposition to belief in God on the ground that religion is harmful. It is a normative position and is logically independent of atheism, since one can disbelieve without regarding belief as damaging; the "New Atheist" writing of the 2000s, and Christopher Hitchens in particular, is its best-known modern expression.
Nontheism covers religious and philosophical positions that operate without a creator god. Theravada Buddhism, Jainism, classical Samkhya, much of Confucianism, and modern religious naturalism and Unitarian Universalism all qualify. Their existence is the strongest available evidence that "religion" and "belief in God" are not the same category, a point that matters whenever general claims are made about religion as such, since a great many of them are in fact claims about theism.