Modding is pretty safe and easy to do as long as the publisher provides you with the appropriate tools.
The best example I can give you are Bethesda's games like Fallout 3, Fallout: New Vegas, Morrowind, Oblivion and Skyrim. Bethesda's games are highly "mod-able". All mods created using their "construction kits" becomes the property of Bethesda.
I've played all the games mentioned above and have modded all of them. Currently playing Skyrim.
Nexusmods.com provides mods for many games for free, just register an account with them. They also have a tool that you can use which will install the mod for you once you have downloaded it; Nexus Mod Manager or NMM. I use this site to get Skyrim mods which has the largest number of mods.
http://www.nexusmods.com/