The one's that seem most prevalent right now are that 1.) We need to have a god to have morals and since we do have morals there must be a god. and 2.) The universe is such an incredibly complicated thing that we can't really know anything for sure. Therefore it's plausible that there's a god.
Neither are sound arguments, obviously.
Those are the main arguments I have been seeing as well and I agree about their validity as arguments. This is what the philosophy professor I asked had to say on the subject,
My own view is that all the arguments are bad. In fact, I am tempted to
say, they are sufficiently obviously bad that only someone antecedently
committed to belief in God would give them the time of day. But there
are very smart people who are still defending one or another of them, so
perhaps I am wrong.
There are articles in the Stanford Encyclopedia of Philosophy on the
main types of argument. These provide a good guide to the recent
literature and can steer you to the best efforts; For example:
http://plato.stanford.edu/entries/cosmological-argument/
More interesting, in some ways, is the idea that religious belief can be
justified by faith and not by reason -- sometimes called 'fideism'.
Some people think that Wittgenstein's later philosophy provides the
tools for working out a version of this -- so we get something called
'Wittgensteinian fideism;. Generally, the people to whom this label is
attached reject it. But I have always found the work of D.Z. Phillips
to be intriguing. Generally, his strategy is to argue that rational
arguments for and against religious beliefs (in prayer, in the
immortality of the soul, in God) are radically beside the point -- they
simply misconstrue the nature of the beliefs in question. Again the
Stanford Encyclopedia's article on fideism is a good place to start.
Russell's book was one of the very first philosophy books I ever read.
I loved it at age 15. I suspect I would love it still.
Howdy, new here.
Wittgenstein stated; 'If you have no words to describe it, it doesn't exist.' Which makes the converse also true.
In my mind thus is simply a differenct phrasing of the ontological argument. I'm not a big fan. Parallel arguments can be constructed to prove the existence of any perfect thing at all.
Well there's the Transendental Argument, also known as TAG. That's a bit tricky, but it's fatally flawed, IMHO. The apologist Matt Slick is a prominent champion of this argument.
The argument basically states that logical absolutes are conceptual, and not dependent on anything material - i.e. matter or no matter, they are necessarily true. Slick tries to divide everything that exists into these two camps, "material" and "conceptual", and since logic isn't material, it must be conceptual, and you can't have a concept without a mind to hold the concept, therefore God.
I think Slick was challenged once with a perceptive question that cuts to the heart of one of the flaws of the argument: he was asked, since everything is either material or conceptual, which category does God fall into? To this he said that God is neither, that God is spiritual.This of course undermines the first assumption of the TAG, which is the dichotomy between either material or conceptual; either this dichotomy is false, or God has to be a material being - either that or just a concept! The latter with which I'll happily agree, but I doubt Slick would find palatable. 
Another objection is that logic doesn't seem to be conceptual either - in that if logical rules (like the law of identity: A=A) are just concepts, then they could conceivably be different. If they are concepts in the mind of God, and God is all powerful, then there's no reason why God couldn't decide that A does not equal A. It seems that these laws trancend even God's concepts.
In a debate with Matt Dillahunty on the TAG, Slick was forced to conceed that the logical absolutes are in fact inherent to God's nature, and that thus God could not change them; God cannot do that which goes against his nature. (This apparently is not a contradiction against his omnipotence.)
My answer to that would be that if logical absolutes can be said to be inherent to God, why can't they be inherent to existence?
Meaning that the basic laws of logic, like the law of identity (a thing is what it is) are inherent features of what it means for something to exist. And that our concepts of these logical laws are just conscious formulations of these inherent rules to existence.
Slick likes to argue that logic isn't something material, you can't go out in the field and dig up a pile of logic and present it to an audience - I would argue that in fact, you CAN do just that!
A pile of rocks represents all the laws of logic as surely as a worded formulation does:
1. Law of identity: The pile of rocks is the pile of rocks
2. Law of contradiction: The pile of rocks is the pile of rocks and NOT (not the pile of rocks)
3. Law of the excluded middle: It is true that either the pile of rocks is a pile of rocks, or it isn't a pile of rocks.
That these aren't spelled out by the pile of rocks is irrelevant: they are physically manifested in their existence - they are inherent to their existence.
Thus is the TAG demolished to my satisfaction, though I doubt anything could ever convince some of it's champions that it's a bad argument.
I have ordered a copy of Bertrand Russell's "Why I am Not a Christian" and it occurred to me that I have not read any recent arguments for the existence of god. For the most part, I usually try to stay away from the thinking that one must ALWAYS give all sides of an argument equal time regardless of their merit, but in this case it is interesting to see what the other side is thinking.
I found this website, not an authoritative site but it lays out the basic arguments on each side in a very understandable manner. The ontological argument for the existence of god is probably my favorite just for the fact that intelligent people have prescribed to such garbage thinking. http://www.philosophyofreligion.info/
I have an e-mail into a former philosophy professor of mine to see if he knows of any current arguments that merit time to read and when he gets back to me I will post his suggestions in this forum.