I equate file sharing to speeding.
If you're doing 80 miles per hour on route 80, you're speeding. However, people will point to the fact that many other people are doing 80 miles per hour, so it's not like they are the only one breaking the law. It's true, but if a police officer pulls you over, it's not an excuse.
Same thing with file sharing.
Sharing and downloading music or movies on the Internet is illegal, if you don't have permission of the person who copyrighted that work. I'd guess that you probably don't have that permission.
Can you get sued? Yes. Can they catch you? Yes. Is it likely? Well, with all the people doing it, it's not likely, but it can happen.
Here's a partial list of people who have been sued:
A 12 year old girl from New York
A grandmother who doesn't know how to file share
Students at Arizona State U.; Marshall; North Carolina State; North Dakota State; Northern Illinois; Ohio U.; Syracuse; U. of Massachusetts, Amherst; U. of Nebraska, Lincoln; U. of South Florida; USC; U. of Tennessee, Knoxville; and U. of Texas, Austin.
Do they have the right to? Yes. When you go on the Internet, every computer is assigned a unique identifier called an IP address. You are assigned one when you connect to the Internet, so if you are online, you can be tracked. If they think you did it, they can get a court order and present that to your Internet service provider, such as Comcast, Optimum Online, or Verizon.
Example Comcast letter
Example Cox letter (another Internet service provider)
Keep in mind that your Internet service provider wants to protect you - after all, you are their customer, and if you broke, you won't be paying for Internet service.