Something that is sometimes mentioned as support for the belief in a god is the so-called anthropic coincidences. Otherwise known as the cosmological fine-tuning argument, this states that even if the origin of all life on Earth can be explained in terms of impersonal natural processes, the mere fact that the universe allows life to exist in the first place is evidence of intelligent design. For instance, for life as we know it to evolve, there must be an unlikely combination of just the right initial conditions and just the right values of a wide variety of physical constants. If any one of the values of several dozen physical constants weren’t "set" to a value extremely close to the actual value we find, then life would not be possible in our universe. The unlikelihood of the universe forming with just the right conditions to allow life by chance is presented as evidence that those conditions were actually set by an intelligent being in order to produce life.
There are a number of issues with this argument. Firstly, it is not at all evident that these constants are so fine-tuned at all. Stephen Hawking says, "The present state of the universe could have arisen from quite a large number of different initial configurations ... so the initial state of the part of the universe that we inhabit did not have to be chosen with great care". We don’t know at present whether all of these fundamental constants are independent of each other. Perhaps it will transpire that there is actually really only one fundamental constant which, once set, determines the values of all of the others. Further, we don’t know what possible ranges of values these constants can take. It may be that the set of possible values is actually very small – making our type of universe not at all unlikely.
Secondly, various multiverse theories that have been proposed by cosmologists that get around the fine-tuning issue completely. According to the 'chaotic inflation' theories of André Linde and others, the expanding cloud of billions of galaxies that we call the big bang may be just one fragment of a much larger universe in which big bangs go off all the time, each one with different values for the fundamental constants. In such a picture, in which the universe contains many parts with different values for what we call the constants of nature, there would be no difficulty in understanding why these constants in our universe take values favourable to intelligent life. There would be a vast number of big bangs in which the constants of nature take values unfavourable for life, and many fewer where life is possible. You don't have to invoke a benevolent designer to explain why we are in one of the parts of the universe where life is possible: in all the other parts of the universe there is no one to raise the question.
An interesting point here is that, as mentioned by Victor Stenger, one needs to introduce additional assumptions in order to prefer a single universe over a multiverse
But, apart from this, perhaps proponents of the fine-tuning argument are guilty of committing the lottery fallacy. If one plays the lottery in the UK, then there is an approximately 1 in 14,000,000 chance of any particular set of six numbers being drawn. So, each time the lottery is run, an event with a one in 14,000,000 probability is going to occur. However, when someone wins the lottery can we therefore infer that the unlikelihood of the event suggests that the lottery is rigged? The answer, of course, is no. Although each particular set of numbers has a 1 in 14,000,000 chance of coming up, there is a 100% chance that one set or other of 6 numbers will be drawn.
Likewise with the anthropic coincidences. Although the chance of the particular set of fundamental constants found in our universe may be infinitesimally small (or, then again, maybe not), some set of fundamental constants may have been inevitable. So, perhaps the fact that there is a particular set of fundamental constants in our universe needs no explaining at all. If the constants were different, then an entirely different type of life might have been pondering the same question.
Of course, the fine-tuning proponent might argue that the true situation is more analogous to buying one lottery ticket, and winning first time – an extremely unlikely event. However, this implies that a universe with us in it is the ‘winning ticket’. Are we really so anthropocentric as to think that our universe is somehow ‘special’, just because it led to us? Actually, I think it would even be difficult to justify the belief that a universe with any type of life is somehow more special than one without. That line of reasoning seems to beg the question. If you specify life as being special – and particularly human life as such – then our universe will necessarily appear to be special. If I roll a die and get a 6, am I then entitled to say, post fact, that a 6 is ‘special’. This type of backwards reasoning is not allowed.
However, even if we assume that a life-producing universe is somehow more special, then we still don’t know how in how many ways a life-producing universe could have emerged from the Big Bang. Perhaps it is not unlikely at all. And, if we look at the subset of all life-producing universes, are we justified in thinking that this particular one is a best case? Our universe is almost entirely lethal to life. By far, most of existence is a radiation-filled vacuum. Life is clearly an extremely rare and unusual product of the universe. We also know it took the universe billions of years to produce any life at all, and then only an extremely simple single-celled life form. Then it took billions more years of a long, meandering and often catastrophically failing process of evolutionary trial-and-error to produce human beings.
So, to conclude, I think that the fine-tuning argument is not at all as persuasive as some believe.