There are three major types: spiral, elliptical, and irregular.
An example of a spiral galaxy:
(SOURCE)
And example of an elliptical galaxy:
(SOURCE)
And example of an irregular galaxy:
(SOURCE)
Galaxies also form clusters and superclusters, the latter of which are galaxies that are not gravitationally bound to one another. Such groups make up much of the structure of the universe.
The Virgo Supercluster includes the Virgo Cluster and the Local Group. Andromeda and the Milky Way are included in the Local Group--and, therefore, us. The Virgo Supercluster's diameter is 33 megaparsecs, which is the equivalent of 110 light years.
(SOURCE)
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Sources:
http://en.wikipedia.org/wiki/Galaxy
http://en.wikipedia.org/wiki/Virgo_Supercluster
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Do you think there's a chance of alien life in one of those billions of galaxies? Do you think people will ever find a way to cross "galactic" distances efficiently?
-----The Golden Eagle