If you are really interested in it, here is the Copyright law:
http://copyright.gov/title17/In general, copyright laws are set up to protect indviduals from having other people exploit their IP for profit. If you infringe on a Copyright, you expose yourself to possible civil action from the rights holders. So lets say you download Anteater, and the guy/gal/mindless corporation that owns the copyright decides you are infringing on the copyright and decide to sue you. What is your exposure? This is assuming that you are not distributing it, that you are using it for home use only and are not using it in a commercial manner. In other words, you aren't spreading it around and trying to make money off of it.
Well they could:
1) Ask for an injunction. Basically get the judge to order you knock it off and stop playing Anteater
2) Ask for it to be impounded - in which case they would try to take the PC away
3) Ask for damages and profits - which is hard, because 1) you aren't making any money off of it; and 2) they aren't making any money off of it either so it would be impossible for them to really prove that you are causing them any damage.
4) Ask for costs and attorneys fees - which is up to the court's discretion.
And this is if they win. In all likelihood you would just get a letter that said "knock it off" because if they went to trial, really the only favorable result they would get is the judge telling you to knock it off.
But I don't want to go to Jail! Well you won't. Its is criminal if
1) You are infringing for the purpose of commercial advantage or private financial gain - assuming its just home use, you aren't
2) You are reproducing or distributing works that have a total retail value of more than $1,000 - you aren't, once again home use, no distributing or reproducing, and it can be argued there is no retail value of anteater, you can't go out and buy it at a retail outlet
3) You make it available or distribute it to the public if you know or should have known that the work was intended for commercial distribution. So lets say that you let people download roms from your website. Well, you are only subject to criminal action if you know that what you are giving away is meant to be sold. This would be up to the feds to prove.
So basically, in the scenario most of us operate in - we acquire roms and play them at home, not distributing them and not making any money off of them, well we are pretty much safe.
Then there are a bunch of other complicated matters, like, if I own a copy of MKII on my Xbox, is it ok then for me to have a copy on my MAME machine? But, long story short:
Think of it like trespassing; if there is this big empty house where nobody has lived in for years and you want to cut across it to go to get to the 7-11, well technically you are breaking the law, you are trespassing on land that you do not own, but most people wouldn't think that is a big deal. This is how I personally view the section of roms owned by dead corporations, or uncertain rights holders. Now If you decide to build a banastand in a busy shopping mall and start selling frozen bananas, well that is a different kind of trespass all together. This is how I view copyrights on games that are still commercially viable.