This isn't a fine tuned explanation of gaming laws and obviously I'm no expert however I will try to get a broad strokes idea out there that's kind of important for game devs, granted it's targeted for the devs that are working with multiplayer and running servers so probably not so indie but all the same it's important.
Basically Health Information Protection Act (HIPA) has been interpreted by the law to include almost all digital data. The basic concept of this is that just because you own the server doesn't mean you own the data on it. All you really need to know about HIPA itself is that it mandates doctors to keep your records private, it's one of many such laws that guarantee your medical privacy. This might not seem like such a big deal at first however if you stop to consider many recent shutdowns of various servers for games and the upsets that they tend to cause you can then understand some of the very interesting court cases coming up lately. Namely a couple different cases by players of these smaller MMO's out there that insist that the items in their inventory constitute digital property and shutting down the server is tantamount to destruction of that property or by restricting access is theft.
My basic suggestion on avoiding that whole thing is a little thing I'm sure you've heard of called a "terms of service" (TOS). You wonder why they exist and you probably always scroll right to the end of them or blindly click accept and move on with your day. This is the very reason those things tend to exist, because by establishing that all the content of the game including the players characters and contents of those characters are your property and that they're being charged a "rental" fee for access to this content, you pre-emptively avoid this entire scenario. One of the most important things I can stress is investing in a good lawyer preferably one who specializes in video game law or entertainment law to draw up a really good TOS for each game, it will save you all kinds of headache.
Assuming you're also an indie dev like myself and can't quite afford such a lawyer then I can suggest looking at the TOS of existing games and software similar to your own and maybe looking up various "free" legal documents online and try to draw one up yourself. You don't have to force people into wasting time on it if you don't want to, rather you can just put a small message or warning somewhere in an intro for example saying that by playing this game they comply to the TOS and then have a link to the TOS in your main game menu or accompanying documents somewhere. Some games just do a small TOS that has broad strokes statements saying they're not responsible for anything and that you can't sue them for any reason related to the game or it's content and you only see it for a second or so on startup. They're strangely effective even though time has proven that unless you're specific then someone will find some creative way around a broad stroke statement like that.
Thankfully there isn't an overwhelming amount of gaming specific laws out there however it's always a solid investment to look at them and related entertainment laws that might effect you, some of them are regional however most are country wide. Laws however are not the only thing to look for, related cases are also important as interpretations of laws by other "judges" constitute 90% or more of what we consider to be "the law" and judges stick together generally upholding existing rulings and using them as direct deferment for similar cases. For example if the content of some game came up regarding the legality of displaying illegal content and behavior or that displaying this game in public during the display of that illegal content and one judge rules that it's covered under existing law establishing it's protected, or prohibited, or any other ruling then if a similar case comes up where the premise is that showing someone doing illegal drugs then it's likely they would defer to the previous ruling and the case would be resolved quickly.
The bottom line is if you're going to get into gaming from a business standpoint it's important to know your laws and disregarding them will always lead to headache down the road.