Is it true that God is real?

As pohnpei noted, there is no definitive answer to this question. He notes correctly that direct, impartial evidence of God's existence cannot be observed; therefore God's existence cannot be proven scientifically. He also notes, however, that God's nonexistence cannot be proven scientifically either; so the question is indeterminate on such grounds.

Many modern philosophers, often arguing from Occam's razor ("do not multiply hypotheses needlessly"), assert that the burden of proof for the claim "God exists" rests with the claimants. Since it cannot be conclusively proven, we must proceed without it. This amounts to acting, in the absence of positive proof, as if God does not exist. This is the position of naturalist philosopher Daniel Dennett, and has been championed in the public sphere by the so-called "New Atheists": Richard Dawkins, Christopher Hitchens, Sam Harris, et al.

Many religious people claim that God's existence is proven by revelation: that a particular text is Divinely inspired or even Divinely written, and by its very nature constitutes proof of God's existence. Other believers claim that their chosen prophet, teacher, etc. is Divinely inspired (or even Divine him/herself). Obviously, these answers are almost entirely subjective; the only standard by which any particular text or person can be judged to be Divine or Divinely inspired is personal experience, which can differ enormously.

Still others will say that God is a matter of faith rather than proof -- that they have faith that God exists, and such faith sustains them through the good and bad of their lives. They are making a consequentialist argument: that one ought to believe in God because it leads to desirable consequences. Another consequentialist argument is the infamous "Pascal's wager": that the penalties for false belief in a nonexistent God are finite, but the penalties for disbelief in a real God are infinite; therefore it is prudent to act as if God exists whether He does or not. Both of these arguments attempt to evade the question rather than answering it.

However, many philosophers and theologians have tackled the question of God's existence over the centuries, with various results. Such arguments usually fall into the tradition of natural theology: the derivation of religious principles from reason and observation alone, without recourse to Divine revelation. Thomas Aquinas famously listed five arguments for the existence of God, most or all of which can be considered special cases of the cosmological (or causal) argument: i.e., that God's existence can be inferred from observation of certain properties of the natural world as a whole -- the cosmos.

Such arguments remain a subject of active study today. A leading contemporary proponent of the kalam cosmological argument (a variation which originated in the Muslim theological school called "kalam", or "discourse") is William Lane Craig. An excellent book which both summarizes and synthesizes the current state of the art in natural theology is A Case for the Existence of God, by Dean Overman. Less technical arguments may be found in the works of C. S. Lewis, particularly the first chapters of Mere Christianity and The Problem of Pain.