If technology continues to improve, we can easily conceive of colonizing the entire galaxy in less then 100 million years. For example, one can conceive of many man made probes sent to a host of other stars. Some will find environments suitable for human life and could clone humans (and other animals and plants) from onboard DNA samples.
Another possibility is that artificial intelligence will develop an exploratory desire and produce machines that can replicate themselves. These machines could travel to neighbouring stars. Those that find solar systems with enough raw materials could go about manufacturing replicas of themselves (or improvements thereof). These daughter probes could then be sent to further multitudes of stars and in a short time the entire galaxy would be completely colonized by these so called Von Neumann probes.
Most of the stars in the galaxy are more than a billion years older than the Sun. If life and civilizations are common throughout the galaxy then they should have colonized the galaxy long ago. Where are they? This is known as Fermi's paradox. Fermi's paradox relies on the assumption that civilizations (as we know them) have a desire to colonize (or at least explore) the Galaxy.