If you love to camp, you'll love backpacking. Basically instead of packing all your stuff in your car and driving to your campsite, and enjoying nature with people all around you, you pack all your gear into a backpack and hike to a remote and way more private location. No neighboring campers playing acoustic versions of their favorite Metallica tunes until the wee hours of the morning.
I would start off slowly and just do an overnight trip. There is a lot less food and water to pack if you are only going for an overnight. I tell you though, chances are high you are going to love it and start planning longer and longer trips. Serious backpackers go for weeks at a time.
Before heading out, it's a good idea to get a book on the basics of backpacking like Backpacking: One Step at a Time ($18.05). It'll give you life-saving tips on how to enjoy yourself in the wilderness, and how to have the least impact on the environment.
Having good gear is essential and you'll need lightweight hiking boots (sneakers are not sturdy enough when you're carrying extra weight on your back), and a good sized backpack. Since you're carrying all your stuff, you want to carry only what you NEED, and you want to get lightweight versions of everything. You'll need a lightweight tent, sleeping bag, and sleeping pad. You'll also need enough food for your trip as well as layers of clothes - warm stuff because it can get cold at night.
Want to see what I pack? Then