I'm not a hammock user myself because a lot of terrain where I camp lacks assured tie-outs (i.e., trees). But in even moderately wooded terrain there are very few places where you couldn't use a hammock (which, in an emergency, can of course be used as an on-ground shelter). Chances are it will be easier to find a spot to hang a hammock than a flat spot to pitch a tent. And hammock users swear by the comfort, breathability, and protection from the elements. (One note: I remain mildly skeptical of the comfort claim, but the Hennessy hammocks are designed to hang very level so you don't feel like a banana.) One knock against hammocks is that they are a little colder than tents because they compress the insulation around the sleeping bag. Not an issue in the summer for most places, but in colder temps pack along a Space Blanket or other heat-reflective item.
Of course, the Hennessey UltraLite wins you savings in the weight department, but not necessarily in the pocket. Well-regarded solo shelters like REI's Roadster ($139; www.rei.com), though about twice the weight, generally cost the same or less yet give you a few more options in varied terrain, as well as a better way to stow and organize your gear.
At the end of the day, then, backpacking with a hammock comes down to personal preference. By all means try one. We tend to get into ruts about gear, such as the belief that we "must" use a tent. There are alternatives, and a hammock is a good one.
Read reviews of solo shelters in Outside's "Friendly Confines" (September '04).