Correction: As pointed out by Durante, this is the whole RAM amount of the system.
eDRAM amount/speed not yet known.
Thanks to Alstrong on B3D and PCPer who did the teardown
TL:DR: Wii U has 2GB of Samsung DDR3 memory running at a max speed of [12.8 GB/s].
PCPer did a teardown. Great stuff... they actually read off the RAM chip (SMRT!). There's only 4 chips.
Samsung K4W4G1646B -> DDR3 4Gbit, 1.5V, 800/933/1066 speed bins -> I'm pretty sure that means "DDR3-1600/1866/2133" data rate.
256Mx16 would imply 16-bit I/O per DRAM... So... 17GB/s at most for main memory bandwidth. They didn't mention the rest of the numbers on the DRAM, but they ought to have high res photos later.
Comparison to other systems by Durante:
Originally Posted by Popstar
17 was a guess based on the maximum speed of the Samsung RAM (1066Mhz vs. 800Mhz). Anandtech unit had slower Hynix RAM.
Originally Posted by Durante
360: 22.4 GB/s + eDRAM for framebuffer
PS3: 25.6 GB/s main memory BW + 22.4 GB/s graphics memory BW, no eDRAM
GTX 680: 192.2 GB/s :P