The right to defend oneself is just that, a right. I don't see why it wouldn't apply, regardless of how times change. The second amendment also exists to keep governments from oppressing it's citizens and allows for the public to revolutionize if it gets really bad. What does 'modernizing' have to do with it?
To say that any right is outdated is to say that all rights in the Constitution are outdated. Just because the physical item has changed over time, does not mean that the natural right becomes null and void. In fact, the advancement of the firearm should strengthen the right to bear arms, as the government and other threats have access to these tools as well as the people. If we took away automatic firearms from the civilian population, then how would they defend themselves against a criminal wielding such a weapon (as criminals do not obey laws, and will find a way to get outlawed arms)? Even worse, how would we defend ourselves if the government decided to move against other liberties, as was seen in Nazi Germany and the Soviet Union during the 20th Century? Civilians may not always "need" automatic firearms, but our nation is built around human rights, not human needs.
Yes, the 2nd Amendment is absolutely applicable in modern America. Overwhelming data has proven over and over again that gun bans lead to more violent crime. Period. This data cannot be disputed. It has remained constant in every single study and across decades of collection by the U.S. Justice Dept. To say that the 2nd Amendment is not applicable in modern America would be to say that human nature itself has somehow changed. It hasn't.
While obviously we don't need to form militias to fend off enemy governments, the 2nd still does apply to modern day as anyone who is familiar with any recent major disasters will know people who can not protect their house or belongings or family is at the mercy of the mob. Hurricane Katrina is a perfect example of where if you did not own a firearm there was nothing you could do to stop anyone from taking everything you owned.