generally lighter than tents or swags even with the tarp as there are no poles to worry about
better ventilation in hot humid tropics
you can get off the ground in wet weather or if there are ground dwelling animals you don't like - less creepy crawlies
better in the mud stays cleaner, just get an armful of leaves to place over the mud under the hammock to help keep you cleaner
they can double as a chair / recliner
don't need to have a clear or flat camp site - can camp over boulders, vegetation or even a stream!
don't have to crawl around on your knees
easier to get in and out at night
better for leave no trace camping (if you protect the tree trunks)
no pressure points as with sleeping on a sleeping mat
may be better for those with bad backs IF you can set it up properly
can set tarp up first in the rain so hammock doesn't get wet when setting up or taking it down - most tents get wet when you set it up or when you take it down in the rain
can stand up and get changed under the tarp
when raining, can cook under the tarp instead of trying to cook in the vestibule of a tent or in the rain
you have better visibility of surroundings compared to a tent with a closed off fly in the rain when you can't see anything