What a great thread! It's nice to see everyone being so supportive and honest.
I too was seriously afraid of the dark, up to the age of 18. Then I just got angry, because it was stopping me camping out solo. So decided I just had to do it. I picked a place on Dartmoor where I could camp at a nice spot, but only a couple of hundred yards from the car, so I could give up and go home if I couldn't bear it. It was a bad night, but a great feeling in the morning, and I haven't looked back. As others have said, experience and familiarity brings confidence.
I spent the last two years living in a caravan in a wood, and was often on my own overnight. I still never watch horror films, and I found that a certain level of preparedness for real dangers built my confidence too. Just simple things like having our grid-ref in my phone so I could easily give it to the police if someone came to rob our sawmill, and knowing exactly what route I would take to retreat unseen out of the wood at night to get to a phone signal. Also thinking carefully about any sort of weapon to hand - mainly because the adrenalin can make you reach for something which could actually only make things worse in most situations. I've seen it happen at a festival once, and that was a good lesson.
Only once did someone come into our camp at night who wasn't supposed to be there. It scared the hell out of me, but because I had previously thought through carefully what I would do in such an event, I was able to control the adrenaline and act appropriately. In the end, I scared the hell out him when I appeared, and I was able to dominate and control the situation.
I still get the heeby-jeebies occasionally, but now that I know the animals and recognise the noises, I love the night. To use Roger Deakin's phrase, the 'wilding quality of darkness' can add much to the experience of nature.