Well... that's, of course, a question that philosophers have been wasting time on for centuries. But I have to admit that my answer is not exactly a brilliantly deep and perplexing thought. I believe I exist because God wanted me to exist.
Uh-oh... Now, there I've done it... I've revealed something about my faith. As a Christian, I believe that God created me (and all of humanity for that matter) to love Him. Seems kinda weird, I realize... But ultimately, God wants us to be His children. He created us, cares for us, gave us everything wonderful that we enjoy, and he wants us to love him back.
You may think: Oh, great... so we're like God's toys or puppets or something. But I don't look at it that way. Aside from all the wonderful things that God gives us as humans, he also gave us something most precious and incredible. Free will -- we can make choices. That's something incredible, but ultimately it makes sense. You can't make someone love you. Love is ONLY by choice. That's why aren't all a bunch of Christians already.
Besides loving my God, I love life. I am here to make the most out of what I've been given and enjoy it to the full.