There are four types of shelters available to the modern backpacker and each has its strengths and weaknesses.
The tent is the most popular shelter but they are almost always the most expensive and heavy option. Nevertheless, because of the protection they provide from critters, bugs, and the elements, they are the most logical choice for extended backpacking trips.
I have had a lot of experience with Bivy Sacks. They are lighter weight than almost all tents and less expensive too. In my opinion they make a lot of sense for the solo hiker on an extended trip. The reason I say solo hiker is because if you are traveling with a companion two bivy sacks weight just as much as a tent all will probably cost more too.
Tarps are ideal for short trips into the backcountry because they are extremely light. However, if you do decide to use a tarp you will most likely also need string and an insect net. And since you were probably going to need some rain gear anyway, you might as well by and oversized poncho and use it like a tarp. This is my preferred shelter on short trips and it saves me a lot of weight.
A Hammock system will weigh about the same as a tent, but it is ideal in warmer weather because you will save weight on a sleeping pad. I must confess that I have not tried this yet, but I hear nothing but positive experiences from people who use hammocks.
Best choice for an extended trip with a companion: Tent
Best choice for an extended solo trip: Bivy Sack
Best choice for a short trip: Poncho
Best choice during the summer (trees required): Hammock