Our Milky Way Galaxy is part of a group of around 30-45 galaxies. This group of galaxies is called the Local Group of galaxies.
In this Local Group of galaxies there are the Small Magellanic Cloud and the Large Magellanic Cloud, which both actually orbit around our Milky Way Galaxy.
The Andromeda Galaxy doesn't orbit our galaxy and is another large galaxy in the Local Group of galaxies.
The galaxies can be categorized by their shape. Some are shaped like spirals (for instance galaxy M33), some are oval or elliptical like M32.