Out of all the religions of the world, what makes Christianity the obvious choice over all the others?
Well, I will take a more apologetics approach since so many have discussed their experiences with God. I'll start with some problems I see with a couple other major world religions that Christianity has the answer to:
Islam: Allah is merciful, righteous, and just. Problem, a just and righteous God must punish sin, and a merciful God must forgive sin. There is no basis within Islam for the forgiveness of sin.
Christian answer: Yehovah is just (Romans 3:26), righteous (1John 2:29), and merciful (Hebrews 8:12). God has satisfied all 3 by sending Jesus Christ to the cross to pay for all mans sins (Psalm 85:10, Romans 3:23-26, Colossians 1:19-20).
Hinduism: The ultimate goal in Hinduism is to achieve Moksha, which is liberation from the cycle of death and rebirth to become one with their god (Brahman), by realizing that they are really just an extension of god. Kharma states that the consequences of ones actions are carried over from one life to the next rebirth, hindering their ability to achieve Mohsha. One can shake bad Kharma through suffering, among other things. If one does a kindness by easing the suffering of another, you upset his kharma and may negatively influence his position in the next life. There is no basis for caring for anothers well being in Hinduism because easing a person's sufferings in this life hurts them in the next. We see this played out in the plight of the lowest rungs of society in Hindu dominated nations (particularly India).
Christian answer: God is love (1John 4:8). Christians are called to show special compassion on those who are oppressed and weak (James 1:27, Isaiah 1:17, etc,etc,etc).
These are but two of the world's religions, but are among the most prominent. I recognize that just because another religion is flawed does not mean that my faith is right; I am simply pointing out that Christianity answers questions that others do not.
Other questions that Christianity answers:
Where did I come from? Genesis 1:1; 27; Ephesians 2:10
What is my purpose/meaning in this life? Matthew 22:36-40; Matthew 25:34-46; Romans 8:29
Where do I go when I die? 1Corinthians 15:35-58; Revelation 21:1-7, etc
There are many more, but I want to at least pretend to attempt brevity.
You might ask; "So why should I trust what the Bible says on these matters?"
Prophecy fulfilled.
I won't even go into the way Jesus Christ fulfilled OT prophecy, I'll just look at a few others that could not have been known at the time of the early NT manuscripts (just in case you believe the prophecies were written after the events they predicted).
Rebirth of Israel as a nation: partial fulfillment of Ezekiel 36-37 (Israel's national faith in God is yet to be revived), required for fulfillment of Ezekiel 38-39
Stop and think about this one for just a moment. Nothing like the return of Israel to their homeland has ever occured in history. They were outcasts among the nations for almost 2000 years, yet still retained their cultural identity. The fact that they even exist as a recognizable people is itself a miracle. Then think of how preposterous it would have been to suggest giving Israel back it's land even 100 years ago. Don't dismiss this lightly.
The ability to have a war that will result in 1/4 of the population of earth dieing through war, disease, and famine: necessary for fulfillment of Revelation 6:1-8
Before this past century, no war, disease, or famine could possible effect the whole world, let alone to this level.
A world economic system that could be totally controled by a single world power: necessary for fulfillment of Revelation 13:16-17
False teachers would forbid marriage and teach to abstain from certain foods: 1Timothy 4:1-3
fulfilled by doctrines of Catholic Church (marriage of priests) and 7th day adventists (forbidding to eat certain foods)]
Possible prediction of effects of nuetron bomb: Zechariah 14:12
Sick, but definitely interesting foreknowledge
Now how about facts of reality that could not have been known at the time of early manuscripts:
Universe had a beginning: Genesis 1:1
Universe shows evidence of expansion: Isaiah 45:12; Jeremiah 10:12; 51:15
Earth is round (much to the chagrin of middle ages church): Isaiah 40:22... word translated as circle is same word used to describe a ball (anything round)
Nations surrounding modern Israel could all unite against them (all Islamic): Ezekiel 38-39
I could go on, but I think you get the picture.