If you start at the center and move outward past the Sun, then you encounter the following arms: the Norma arm, the Scutum-Crux Arm, the Sagittarius Arm, the Perseus Arm. The Local Arm that the Sun happens to be in is not a full arm. There is also a piece of arm called the Outer Arm, but that seems to be a part of the Norma Arm. These arms (except for the Local and Outer Arms) are named for the constellations that contain them (as seen from Earth).
At the end of 2003, Australian astronomers from CSIRO reported that they discovered a new piece of spiral arm at 15 - 20 kpc from the center. It is very well possible that this is yet another part of the Norma Arm, at yet greater distance from the center than the Outer Arm, which also seems part of the Norma Arm.
The spiral shaped arms seem to be the effect of density waves moving outward from the center of the Galaxy.
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