Well I only say 4GB assuming the next console will have a lifespan the length of the 360; so that would future proof it. Also, when 4k resolutions and displays come into play we will be glad if it's 4GB not 2GB ha
There's no way the Xbox 720 will have the graphics power required for 4K resolutions, as even top-end dual-GPU PC setups can't manage that. It's very unlikely you'll even see 2K resolutions supported, even for graphically simple games. And that's without even factoring in the adoption rate of 2K/4K displays, which aren't as well supported as 1080p was at the launch of the X360 (and 720p was still in its infancy).
I wouldn't be surprised to see 2GB or less, as that would be up to four times the amount seen in the X360 and the speed will be considerably faster. The largest benefit could come from using SSD storage or a SSD/HDD hybrid drive, which would take a lot of pressure off the system memory. All they need is enough memory to handle 1080p in 3D (120Hz), with a little bit more for "future proofing" (as if such a thing is even possible).
I'm expecting to be underwhelmed with the specs of the next generation of consoles, as I really think they'll do the bare minimum needed to support 1080p / 3D. Sony took big losses last generation and Microsoft doesn't want to price itself out of the market either. With Microsoft looking to make Kinect mandatory - at least according to the last rumours I saw - I think they're looking to move away from sheer horsepower and focus on the experience.