a•pol•o•get•ics n. (used with a sing. verb)
Apologetics are the works attempting to justify belief in god in some way. More generally, they are works attempting to justify any belief or belief system.
Although the Western world is predominantly occupied with apologetic works defending Christian doctrines, the term is of course wider.
Apologetics is the religious discipline concerned with the application of theology to the real world. It typically consists of taking any one of the many areas in which theology does not match up with reality, and producing extremely verbose explanations for why it's reality that's got it wrong. 
Canvassing the entire breadth of apologetics is a monumental task. Following the example of An Index To Creationist Claims, we will instead slowly construct a hierarchical list critically reviewing all theistic claims. In addition, our list will include apologetics for Naturalism, arguments attempting to demonstrate the plausibility and justifiability of naturalism.
In the following "god" takes various meanings, as appropriate to the specific argument. Usually the god of classical theology is addressed, a being that is omniscient, omnipotent, perfectly moral, a person, simple, and the creator of everything. More generally, the arguments support naturalism and oppose any sort of supernatural entity and even natural entities of immense power. Certain arguments also address very specific gods, such as the Yahweh of the Old Testament, Zeus, and so on.
1 Philosophical Arguments for God
These are arguments that rely on little, if any, empirical input and evaluation. Instead, they try to argue from first principles, taking perhaps only arguably-philosophical principles (such as causality) as given. These also includes more evidence-based variants of the main arguments, however.
1.1 The Ontological Argument argues that god exists by definition.
1.1.1 Alvin Plantiga's Modal Argument
1.2 The Cosmological Argument argues that an Ultimate Cause, which is associated with god, exists.
1.3 Transcendental Arguments argue that some feature of the world cannot be without god.
1.3.1 The Argument from Reason attempts to show that reasoning is impossible without god.
126.96.36.199 The Evolutionary Argument Against Naturalism is a variant of the argument from reason, albeit an evidential one.
1.3.2 The Argument fom Absolute Morality says morality is impossible without god.
1.3.3 The Argument from Purpose or Meaning claims neither is possible without god.
1.4 Pascal's Wager attempts to convince us to wager on god's existence.
1.5 The Argument from Contingency stems for questions such as "Why are things the way they are?" or "Why is there something instead of nothing?"
2 Evidential Arguments for God
These arguments rely on at least a low level of input from empirical sources.
2.1.1 The Anthropic Argument asserts that features of the world are directed to support human life.
188.8.131.52 The Fine Tuning Argument asserts that the constants of physics are fine-tuned to support life.
2.1.2 The Argument from Desire argues that our desire for god indicates that god exists.
2.2 An Argument from Miracles is any argument that refers to real or purported real-world events as evidence for supernatural intervention.
2.2.1 The Argument from Natural Signs sees natural events as indicating supernatural agency.
2.2.2 The Argument from Prophecy alludes to supernaturally-acquired knowledge.
2.3 The Argument from Beauty argues that beauty indicates the divine.
2.3.1 The Argument from Cosmic Beauty argues that the beauty of large-scale features of the universe indicates a divine anthropomorphic creator.
2.4 The Argument from Personal Experience argues from personal revelation.
2.5 The Argument from Laws of Nature argues that laws require a legislator, which is god.
2.6 The Argument from Authority relies on various people or scriptures as authoritive.
2.8 The Argument from Atheistic Evil argues that atheism is detrimental.
1 Philosophical Arguments Against God
1.1 Arguments from Logical Impossibility argue that certain conceptions of god are simply self-contradicting.
1.2.1 The Burden of Proof
1.2.4 Dawkin's Evolutionary Argument Against God
1.3 The Argument from Realism argues that all reality is at the same level of existence.
1.4 The Argument from Psychological Appeal argues for a negative bias to forestall our natural tendencies to adopt appealing views.
2 Arguments from Evidence
2.1 The Argument from Hiddeness argues that no god is apparent.
2.2 The Argument from Evil argues against the possibility of a benevolent god.
2.3 The Argument from Scriptural Inaccuracy argues against specific scriptures as being god's word.
2.4 The Argument from Religious Evil makes the (fallacious) argument that religion breeds evil so should be disbanded.
2.5 The Argument from Anthropomorphism argues that an anthropomorphic god is a priori unlikely. 2.5.1 The Santa Claus Argument argues that belief in God is as naive as belief in Santa Claus, and should be rejected for the same reasons.
2.6 The Argument from Non-Anthropocentrism argues that a personal god interested in humans is unlikely.
2.7 The Argument from Causal Closure argues that there is no place for god in the causal chain.