For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
But let's look at it in context.
Just before Jesus (supposedly) spoke these words, he (supposedly) said:
And as Moses lifted up the serpent in the wilderness, even so must the Son of man be lifted up: That whosoever believeth in him should not perish, but have eternal life. John 3:14-15
That's right. Jesus believed in the snake-on-a-pole story of Numbers 21, God's 23rd Killing. He believed that God sent fiery serpents to bite and kill the people for complaining about the lack of food and water. And he believed that God told Moses to make a brass serpent and put it on a pole so that those who looked at it would be magically cured. And he was OK with all that.
In fact, Jesus said his own death would be just like that. If you believe in Jesus' magical death, you'll be saved just like the people that had been bitten by God's fiery serpents were saved by looking at Moses' magic snake on a pole.
But what if you don't believe in Jesus' death any more than you do in Moses' magic snake pole? Well, here's what Jesus supposedly said right after the famous words of John 3:16.
He that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God. John 3:18
And, a little later, in John 3:38:
He that believeth not the Son shall not see life; but the wrath of God abideth on him.
So let's put John 3:16 in context. If you believe in Jesus and in Moses' magic snake pole, you'll go straight to heaven after you die. If not you're going to hell.
Thanks to matt311 and wise fool for pointing out Jesus' belief in the cruel and stupid story in Numbers 21.