A galaxy is simply an aggregate of stars, gas, and dust. They vary immensely in size, containing from as little as a few million stars to as many as several trillion; they can measure from a few thousand light years across to as many as several thousand light years. There are four basic shapes for galaxies -- spiral, elliptical, lenticular (i.e., shaped like a lens) and irregular.
Spiral galaxy M100
Elliptical galaxy NGC 1316
Lenticular galaxy NGC 5866
Irregular galaxy M82
All illustrations on this page courtesy of NASA and the Hubble Space Telescope.