Microsoft's XBox Live, Blizzard's Battle.net, and Grinding Gear Games are among others to have reported being disrupted over the weekend.
The attacks coincided with a bomb scare involving a flight carrying a Sony executive.
John Smedley, president of Sony Online Entertainment, had been tweeting about his firm's efforts to combat a "large scale DDoS" before posting a message saying he was about to board the plane.
DDoS (distributed denial of service attack) - a technique in which many computers are used to flood an online service with requests in an attempt to overload its systems.
A Twitter account that has claimed responsibility for attacking Sony and the other video games firms has linked the attacks to the jihadist group Islamic State, posting: "Kuffar [non-believers] don't get to play videogames until bombing of the ISIL stops."
It also makes several references to Isis - the former name used by the Islamic militants.
The incidents follow reports of earlier DDoS attacks on other multiplayer titles on Friday, including Eve Online, League of Legends, RuneScape and Guild Wars 2.
