Earlier quoted context omitted.
Yes. But Romeo and Juliet apparently borrowed heavily from works from 1562 and 1582[1]. Since he wrote the play in 1591, both works would have been under today's copyright. [1]: http://en.wikipedia.org/wiki/Romeo_and_juliet
"borrowed heavily" != copied verbatim. How many hollywood movies feature extremely similar plots?
IANAL, but I personally have no doubt that Shakespeare would have been sued if today's copyright culture had existed then. He even copied the characters' names (and yes, characters can be covered by copyright), not to mention most of the major plot elements. It wasn't just "Oh, this general idea is kinda similar to that one."
It's the skill of Shakespeare's story telling that made him so great, not the stories themselves. But the stories are protected by copyright, not the skill.