The intended conclusion to logical arguments for the existence of God. The following is an example of such an argument:
1) If objective morality exists, then God exists.
2) Objective morality exists.
3) Therefore, God exists.
The following argument, although popular in Christian apologetics, is not an argument for God's existence:
1) Everything that began to exist was caused to exist.
2) The universe began to exist.
3) Therefore, the universe was caused to exist.
This argument, the Kalam Cosmological Argument, is technically not an argument for God's existence, because the cause called for in premise 3 could be anything from an impersonal cause to a cosmic Bozo the Clown. Furthur premises are required in order to call this an argument for God's existence, to wit:
4) The universe's cause cannot be anything other than God.
5) Therefore, God exists.
Some apologetic arguments -- specifically many versions of the Transcendental Argument for God -- do not argue for the existence of God, but from the existence of God. As one TAG proponent put it, "God is always the beginning, never the conclusion." Such an argument goes like this:
1) God exists.
2) Therefore, logic/science/morality/whatever exists.
This type of argument leads to some nifty rhetorical devices, such as, "Simply by agreeing to this debate, the atheist has conceded it, because that act, and every act, presupposes the existence of God." Atheists, however, are unimpressed with such circular logic.
There are many resources which contain lists of arguments for God's existence, both valid and invalid. One such resource is Alvin Plantinga's "Two Dozen (or so) Theistic Arguments."(1) A much more massive (and much more unsympathetic) resource is the TGE Project, whose website(2) contains, as of this writing, over five hundred arguments, all (or almost all) with the conclusion, "Therefore, God exists." Examples of their list entries include:
1) I define God to be X.
2) Since I can conceive of X, X must exist.
3)Therefore, God exists.
1) If things had been different, then things would be different.
2) That would be bad.
3) Therefore, God exists.
1) Colors exist, and are in part caused by the physical properties of objects.
2) Let's not think about how this could have come about without God.
3) Therefore, God exists.
1) Simple explanations are generally better than more complex explanations.
2) The universe can be explained as the creation of God, a being who is omniscient (where omniscience is defined as having all knowledge of true propositions knowable by an Anselmian supreme being in all possible worlds which do not imply weird McEar paradoxes), omnipotent (where omnipotent is defined as having the ability to do any and all logically possible actions coherent with the idea of a supreme being and those by unsupreme beings), morally perfect (where morally perfect is defined as being of a perfectly good will and only does good actions, and only allows good actions or those actions which lead to even better results), immaterial (where immaterial is defined as not being composed of matter or described by physical laws of any logically possible world, including those comprising nothing physical), and a person (where person is defined as having intellect, intent, will, and worthy of moral respect and able to make moral decisions), and this is a fully simple explanation, given the simple and immediately understandable (by anyone) definition of God (where simple is defined as having a nature identical with his existence, and all properties of X being identical to any other properties of X, and these properties not identical to any other beings other than X).
3) Therefore, God exists.
It is widely believed that the TGE Project is actually a branch of the Evil Atheist Conspiracy, but this has not been proven.
Sources:
(1) http://www.homestead.com/philofreligion/files/Theisticarguments.html
(2) http://facts4god.faithweb.com/thelist.html