We always had wrapped gifts and so did DH's family. Aside from the big items, like bikes. I never knew another way, until my friend in another state told me thats how they did it, and she showed me a picture of her kids faces that she caught when they woke and saw the presents, it was priceless. I however still like the idea of wrapped gifts.
When I think back to my childhood I think of how much fun it was to tear into the paper. I now enjoy watching my children tear into the paper. I also think of how, my brother, sister and I would wake early and sneak downstairs before our parents were awake. Had the gifts been opened, my parents would have missed the surprise. So for me, I'm sticking to wrapped gifts.
Edit to Add:
FYI: Lynn M. our Santa always hid our bigger gifts. We had a screened in porch and after our little gifts were unwrapped, mom and dad would say oh wow, what is that on the porch....or one year we had a note they left for us we found after opening up gifts where to find the unwrapped big gift.