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. - John 3:16 (KJV)
This is the version most of us are familiar with - but I think the wording in this version is misleading, or at least incomplete. To be fair, it's worded this way in a number of versions. The common understanding isn't horrible, but I think it misses something.
When John says that God so loved the world, he isn't saying God soooooo loved the world. In other words, it's not the same meaning that your grandma would have in mind if she said it. John was not trying to communicate that God really, really, really loved us, though that is how I think we usually read it. John was trying to communicate how God loved us.
I think the NET version of the Bible is helpful here. Check out John 3:16 in the NET Bible:
For this is the way God loved the world: He gave his one and only Son, so that everyone who believes in him will not perish but have eternal life.
Or in Wuest's Expanded Translation:
For in such a manner did God love the world, insomuch that His Son, the uniquely-begotten one, He gave, in order that everyone who places his trust in Him may not perish but may be having life eternal.
There are other versions that translate along these lines as well. This phrase "so loved" ought to be read as “this is how much”, or “in this way.”
Does this explain how much God loves us? Yes, but it does so by illustration not hyperbole. You can think of it like this: "God has shown his love to the world in this way." In what way? From the prior verses, much like the way Moses lifted the snake in the wilderness. He loved the world by giving His Son to be lifted up on a tree for the salvation of mankind.
Is this to say that the traditional understanding is blatantly wrong? I don't think so. The common view doesn't do any real damage to Christian doctrine. That said, I think this view gives us a richer understanding of God's love and its expression.