Games frequently have embedded video. Said video could be at any frame rate, but is usually either 24p or 30p.
The actual game content is usually locked 30p or 60p, but can vary based on visual content and the performance of the console or PC.
Some PC monitors are honest 120hz displays that take 120hz inputs. On that kind of monitor you can play games at up to 120p depend if you've got a powerful graphics card.
So to sum up, frame rate for video games (during play) has no standard, because it's not even fixed. With V-Sync off, on the PC you'll render frames as fast as you can. But you'll always be limited by the refresh rate of the monitor which for 99% of LCDs out there is maxed out at 60hz.