The answer to this question is a bit complicated, it depends on which type of Daddy-long-legs you’re referring to. There is a group of spiders that are sometimes known as Daddy-long-legs, these are the cellar spiders of the family Pholcidae. These are the guys you can usually find hanging around in the corners where the walls meet your ceiling, they are responsible for the cobwebs in most homes. They are true spiders so they have two body parts (an abdomen and a cephalothorax to which their eight walking legs are attached).
Another group of animals which are closely related to spiders are the Harvestmen (also called Opiliones), they are also commonly referred to as Daddy-long-legs. They can be distinguished from spiders by the fact that they have only one body part to which their legs are attached. If you watch them walk, you’ll see that they have only six walking legs, the second pair of legs are extra long and are waved about in front of the harvestman feeling (and tasting) the surroundings.