Here's a list of the most common (and to my mind, the most persuasive) arguments for God's existence, and their single best defenders and their work.
1. Cosmological Argument(s)- Alexander Pruss, no doubt about it. This (very underrated) metaphysician has developed Leibniz's cosmological argument from contingency to terrifying detail. Each of the premises in his version of the argument gains their support from multiple contributing lines of evidence. Most impressive is his thorough, uncompromising defense of (some version of) the Principle of Sufficient Reason (basically a nuanced form of the causal principle- all things that can have causes do have causes), to which he has dedicated an entire book. To put this in perspective, William Rowe- one of the leading atheist philosophers of the current generation, famous for his 1979 formulation of the evidential argument from evil- said the only weakness of the cosmological argument is that the PSR isn't well-defended enough. I wonder if Rowe has read Pruss' book since then?
Pruss' long essay in the Blackwell Companion to Natural Theology deals with virtually all objections that can be thrown at the contingency argument, and- in my opinion- summarily disposes of them.
That's not all, however. He has a new book coming (co-authored with another illustrious defender of the cosmological argument, Joshua Rasmussen) entitled Necessary Existence where the authors argue for the existence of at least one Necessary existent concrete being. In addition, he has also started working on a book which debunks the claim that all contingent reality can be explained by a chain of contingent events extending infinitely back into the past. This, by the way, happens to be the key
I should also mention Emanuel Rutten's PhD thesis. This book deserves mention because the author takes on particularly difficult objections to the cosmological argument, and provides rather out-of-the-box solutions for them. His work incorporates a lot of insights gleaned from mereology, based mostly on Kathrin Koslicki's work. The perfect demonstration of the cosmological argument would emerge if it were possible to merge Rutten and Pruss' work into one beautiful, thorough, coherent thesis.
2. Fine-tuning argument- Robin Collins, very little doubt about it. What makes Robin Collins' work impressive is his uncompromising incorporation of both heavy-handed physics/cosmology as well as cutting-edge philosophical insights. His essay in the aforementioned Blackwell Companion is widely regarded as the best defense available for the fine-tuning argument. He calls this essay a "highly abridged" version of the much-awaited forthcoming book-length treatment of the argument. There was supposed to be one book, but he decided to write two books- the first one on how the fine-tuning evidence is better explained on theism compared to the single-universe hypothesis, the second one dedicated only to the multiverse hypothesis (here are some of his articles on both topics).
A significant feature to take note of is Collins is making a cumulative case design argument based on two discrete lines of evidence- the habitability of the universe, and the discoverability of it. In other words, his argument is not only that many of the universe's constants are fine-tuned for life, but also that many of its features are fine-tuned for us to do science. The universe is anthropically user-friendly. Does this seem reminiscent of the Qur'an's appeals to the sun, the moon, and the stars being created for, among other things, keeping track of time and knowing directions at night?
The only thing about his argument one can bat an eyelash at is the fact that his argument is inductive, as opposed to deductive. They adopt a variation of the "inference to the best explanation" scheme- by ruling out naturalistic single- or multi-universe hypotheses, the only real contender are theism, deism or axiarchism of some form. People who are more fond of deductive argument schemes may be a little perturbed by this. The only scholar that I know of to make a deductive argument mechanic to run the fine-tuning argument is William Dembski. William Lane Craig in his formulations of the fine-tuning argument seems to adopt his argument scheme. I haven't studied this scheme in much detail (I'm not a math person), but it definitely needs to be looked into. Perhaps one reason why it hasn't received serious philosophical attention is because it has been used in the defense of intelligent design arguments, something philosophers tend to steer clear of due to the embroiling controversy. Just as a trivia, Robin Collins is critical about the design inference scheme, but Dembski claims to have put his concerns to rest in his book No Free Lunch. I have read neither sides of this debate so can't really tell who's got the better side of the argument.
I think I should also mention Luke Barnes in connection to the fine-tuning argument. His treatment of the more common objections to the fine-tuning argument demonstrates an admirable level of clarity. People looking to get an introductory taste of the argument from fine-tuning is welcome to listen to this podcast episode. There might even be a book on the way...
3. Argument from religious experience- Just to be straight, this is not an argument for theism, or even deism. All this argument purports to show is that there is a supernatural realm beyond this sticks-and-stones physical reality (i.e. naturalism is false). I believe the best defense comes from Stephen Braude. As is the case with Robin Collins, his work is impressive because he incorporates insights from both parapsychological/paranormal investigations as well as stone-cold philosophy. This combination is unique when it comes to the paranormal, where the popular authors are more interested in throwing data out in the open without classifying, categorizing, or responsibly interpreting it. Braude's treatment of the topic is very, very careful and, as far as I can tell, philosophically airtight. I'm currently reading his book ESP and Psychokinesis: A Philosophical Examination, where he examines different kinds of paranormal phenomena and writes about their philosophical import. Another interesting book by the same author is Immortal Remains, which is a long, sustained argument for the reality of life after death. This interview is a nice brief introduction to his work.
4. Arguments from biological design- As I see it, there are lots of great material on the arguments from biological design, but they are scattered all over the place. Both books (Signature in the Cell and Darwin's Doubt) by Stephen Meyer are very well argued. There are also well-researched works that disprove the standard Neo-Darwinian narrative, e.g. the ones by James Shapiro and Marcello Barbieri). Papers in the Bio-complexity journal seem like really good material as well. What's lacking here is synthesis. There needs to be a concerted effort to synthesize all the myriad forms of biological design arguments, and defend this synthesized version with sufficient philosophical rigor. This synthesis also needs to work as a research program for biological design features, because new data about biological design just seems to accumulate. There needs to be a research scheme or structure to incorporate all this data. That, I think, is the major shortcoming (as well as the holy grail) as far as biological design arguments are concerned.
- J. P. Moreland, the argument from consciousness
- I can think of quite a few other names, but I don't think they match the caliber of the scholars I've mentioned here.