Skull-and-Crossbones
If you're looking at a historical example of the skull and crossbones, you may be looking at Edward England's pirate flag. The skull itself often represented either a death threat, or the devil himself. The typical design for flags is one skull facing forward, with a pair of bones crossed at the bottom. Christopher Condent also had a similar design: three jawbone-less skulls and crossbones in a row.
Sideways Skull
The sideways-looking skull is a variation. Henry Avery is a famous pirate whose flag looked like this. He also sometimes used one with a red background instead.
Crossed Swords
A variation of the skull-and-crossbones used by "Calico Jack" Rackham had the smiling skull on it, over a pair of crossed swords.
Inset Bones
Some flags used a variation of the skull-and-crossbones design that set the bones behind the skull flag. The basic version of this was used by Richard Worley. There was another version used by Emanuel Wynne, which had the inset bones design over an hourglass--a typical pirate symbol that evokes the grim reaper.
Arm and Sword
Thomas Tew is another famous pirate whose flag actually went away from the skull motif altogether. On his flag, a muscular arm is curled and bears a large sword.
Skeletons
The full skeleton design is a much more complicated pirate flag, but it was also used by a few pirates. Pirates like Edward Low, who used a red skeleton on a black flag, used it for the same death threat as the skull. Edward Teach, better known as Blackbeard, had a variation of this flag: the skeleton wears a crown and bears a spear which he stabs at a bleeding heart.
Combination Flags
Many of the images on pirate flags were constructed from other, smaller images. A pirate named Christopher Moody, for example, had a red flag with an hourglass on the right, a sword-bearing arm in the center, and a skull and crossbones on the left. Walter Kennedy used a skull and crossbones next to a muscular man figure with an hourglass and sword. There was also Stede Bonnet's flag, which depicted a scale, a skull and a heart, all underlined by a bone.
Black Bart
Bartholomew Roberts, sometimes called "Black Bart," had one of the few flags to have a self-portrait in both of his main variations. In the main flag, he is shown toasting or sharing an hourglass with a spear-bearing skeleton. In the other, he is standing upon two skulls with the initials "ABH" and "AMH," which stand for "A Badbadian's/Martinician's Head" in reference to his long-standing feud with the people of Martinique and Barbados.