This question has taken on increased importance with the discovery of
giant planets close to their primary stars.  It is thought that these
giant planets did not form this close to their host stars but
migrated.  (See the FAQ entry on the formation of the solar system.)
In general, the possibility of migration has alerted (or re-awakened)
astronomers to the possibility that a planetary system can change over
time.  If a giant planet migrates inward from the position at which it
formed, it can scatter terrestrial planets.  These terrestrial planets
might plunge into the host star or be kicked into interstellar space.
(Another possibility, though probably even less likely, is for a
passing star to disrupt a planetary system.)

What would happen if the Earth were kicked into interstellar space?
Life on the surface would certainly be doomed as it gets its energy to
survive from the Sun.  In fairly short order, the oceans would freeze
over.  However, the Earth is still generating heat by radioactive
decay in its interior.  Some of this heat leaks out through
hydrothermal vents on the floors of the oceans.  Thus, the lower
levels of the oceans would remain liquid, and the hydrothermal vents
would remain active.  Organisms that depend only on the hydrothermal
vents could survive probably quite happily for several billion years
after the Earth was ejected from the solar system.  (Indeed, since the
oceans will probably boil away in the next few billion years as the
Sun's luminosity increases, these organisms might prefer the Earth to
be ejected into interstellar space!)

For additional reading see "The Frozen Earth" by Adams & Laughlin,
<URL:
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1999AAS...194.1511A
> and Stevenson, "Life-sustaining planets in interstellar space?",
Nature, v. 400, 1 Jul 1999, p. 32.