http://en.wikipedia.org/wiki/Quinque_viae#Criticism
The five logical reasons God exists.
the unmoved mover;
the first cause;
the argument from contingency;
the argument from degree;
the teleological argument ("argument from design").
Sure, there is criticism from people like Richard Dawkins
http://en.wikipedia.org/wiki/Quinque_viae#Criticism
However, to quote here:
http://en.wikipedia.org/wiki/Quinque_viae#Defense
The 20th-century philosopher of religion Richard Swinburne argued in his book, Simplicity as Evidence of Truth, that these arguments are only strong when collected together, and that individually each of them is weak
Philosopher Keith Ward claims in his book Why there almost certainly is a God: Doubting Dawkins that Dawkins mis-stated the five ways, and thus responds with a straw man. Ward defended the utility of the five ways (for instance, on the fourth argument he states that all possible smells must pre-exist in the mind of God, but that God, being by his nature non-physical, does not himself stink) whilst pointing out that they only constitute a proof of God if one first begins with a proposition that the universe can be rationally understood. Nevertheless he argues that they are useful in allowing us to understand what God will be like given this initial presupposition.[9]
More recently the prominent Thomistic philosopher Edward Feser has argued in his book Aquinas: A Beginner’s Guide that Dawkins, Hume, Kant, and most modern philosophers do not have a correct understanding of Aquinas at all; that the arguments are often difficult to translate into modern terms; and that the Five Ways are just a brief summary directed towards beginners and must be understood in the context of Aristotle’s Metaphysics and Aquinas’ other writings. He argues that Aquinas’ five ways have never been adequately refuted when thus considered.[10]
Eastern Orthodox theologian David Bentley Hart says that Dawkins "devoted several pages of The God Delusion to a discussion of the 'Five Ways' of Thomas Aquinas but never thought to avail himself of the services of some scholar of ancient and mediaeval thought who might have explained them to him ... As a result, he not only mistook the Five Ways for Thomas's comprehensive statement on why we should believe in God, which they most definitely are not, but ended up completely misrepresenting the logic of every single one of them, and at the most basic levels."[11] Hart said of Dawkins treatment of Aquinas' arguments that:
Not knowing the scholastic distinction between primary and secondary causality, for instance, [Dawkins] imagined that Thomas's talk of a "first cause" referred to the initial temporal causal agency in a continuous temporal series of discrete causes. He thought that Thomas's logic requires the universe to have had a temporal beginning, which Thomas explicitly and repeatedly made clear is not the case. He anachronistically mistook Thomas's argument from universal natural teleology for an argument from apparent "Intelligent Design" in nature. He thought Thomas's proof from universal "motion" concerned only physical movement in space, "local motion," rather than the ontological movement from potency to act. He mistook Thomas's argument from degrees of transcendental perfection for an argument from degrees of quantitative magnitude, which by definition have no perfect sum. (Admittedly, those last two are a bit difficult for modern persons, but he might have asked all the same.)"[11]
Quoted from Wikipedia