That heavily depends on how high you want your settings. Playing in HD (1920x1080) for example is a lot more demanding than other, lower resolutions. It also depends on the settings you chose ingame (shadows, details etc).
It also depends on which games you are playing. Let's take a look at the system requirements of Watch Dogs, a AAA title coming next month for PC, PS4 and Xbox One (also for the old gen):
Minimum:
CPU: Intel Core 2 Quad Q8400 @ 2.66Ghz or AMD Phenom II X4 940 @ 3.0Ghz
RAM: 6 Gigabyte
DirectX: DirectX11
GPU: 1024 VRAM DirectX 11 with Shader Model 5.0
HHD: 25 Gigabyte
Recomended Systemanforderungen:
CPU: Core i7 3770 @ 3.5Ghz or AMD FX-8350 @ 4.0Ghz
RAM: 8 Gigabyte
DirectX: DirectX11
GPU: 2048 VRAM DirectX 11 with Shader Model 5.0 or higher
HDD: 25 Gigabyte
As you can see, pretty demanding. An eight-core CPU is recomended since the new console have 8-core technology as well. These requirements are tough, but you have to expect them for the upcoming AAA-titles like Watch Dogs, The Division and so on.