How much GPU memory do iPhones and iPads have?

iPhones/iPod Touches/iPads all have a Unified Memory Architecture which mean that both the CPU and GPU share system memory. There is no dedicated video memory on these devices.

The advantage is that you don't need to worry about running out of video memory for your textures or vertex data (your app will be terminated by iOS for using too much memory before that happens). The disadvantage is that you share the same memory bandwidth for gameplay and graphics. The more memory bandwidth you dedicate to graphics, the less you will have for gameplay and physics

On the newer processors such as the A5X, A6 and A6X Apple has doubled the bandwidth to memory for the GPU to 128bit whereas the CPU still has 64 bit access.