In default minecraft, no. We as a community roleplay and create them using mods and plugins though.

I've never played Minecraft but this looks really cool. Is there some sort of quests or stories to be played in Minecraft?

We did so through minecraft for a server we run, Here's an album of pictures I took of our builds. 

http://imgur.com/a/4JUIE

X post to /r/minecraft - http://www.reddit.com/r/Minecraft/comments/33ed7h/some_friends_and_i_recently_put_together_a_roman/

Not sure if you're interested in this sort of stuff, but my friends and I tried to make a Roman styled city.