Ok lets say theirs a site for example called target.com. I make a site called targets.com Target.com has a business with their named copyrighted any everything. Can they sue me for making targets.com?
It's "trademark" not "copyright". If you made a site in the same business as them and/or tried to trade off their name they could sue or take you to ICANN's UDRP court. http://www.icann.org/udrp/udrp-policy-24oct99.htm
For most cases, no. The term "target" is generic. However, if you show signs of "bad faith," then they can take actions against you.
One can't show signs of "bad faith" if the term is generic to begin with. On the other hand, it isn't often a question of whether it's generic or not, but how it's intended to be used.