There are mainly three types of galaxies:
elliptical, spiral, and irregular.
Elliptical galaxies can look anywhere
between elongated to spherical. There is not much
structure to these galaxies, nor is there much gas
or radiation between systems in these galaxies.
Spiral galaxies look like pinwheels,
with spiraling arms coming from the center, and
most of the stars and visible matter are
concentrated on one plane (think disk-shaped).
Irregular galaxies are those that
cannot be called either spiral or elliptical.
There are also a few other minor types that do
not appear often, at least as far as we can see,
such as ring galaxies.