Like "Food" said, comfort. I don't think I've camped in a tent in 15 years. Hammocks just suit me..I sleep better in a hammock than my bed at home. I didn't become curious about hammocks because of backpacking/camping. While in Cozumel, Mexico, I visited our guide's home and there were net hammocks strung up all over, no beds. So, I bought a couple and tried them...then took them camping. There is one on my back porch now. I considered the Mexican hammocks a bit on the heavy side and made my own from ripstop, using a plastic tarp as a fly.
Then Hennessey came along and that's what I've been using.
The fact that you can pitch them on the ground like a tent is an added benefit, if you run out of trees.
As "food" indicated, its quite nice not having any ground concerns at all. As long as you have rope long enough to connect two trees, you're good. My wife loves 'em too.