From my research and what I have been told by others, the only way you have reason to worry about downloading copyrighted material are if -
1. You download tons of gigs a month, I'm talking about 1000's of gigs per month or more. I think your ISP could see an influx of downloading and possibly turn your address over for suspicion. Casual downloaders who download 10 or 20 gigs a month have nothing to fear in that area.
2. This is probably the main thing people have to worry about and that is if you sell bootlegged copies of material. Then you should worry as you could be watched by federal agents. This imo only applies if you sell a lot of bootlegged copyrighted material.
Also I don't feel it matter the nature of the download be it music, movies or games. It's all the same and by that I mean one is no worse then the other.
I have heard of people being sent letters from their ISP with a list of the things they downloaded and what they would cost in a store along with a bill for the total amount. This is something that happens rarely though.
Being busted for downloading copyrighted material is something I would bet none of us has to worry about though.

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