Hi Mark.
When you are trying to build for Android, you will quickly find that a) they don’t use any Apple screen sizes for the most part. You will also find that Android device makers don’t maintain any sense of resolution or even aspect ratio. They kinda get close with something close to 16:9, but they are all off just a hair. Most developers want apps to fit perfectly.
But if you think in generalities, there are four common shapes. The more square/wide iPads with an aspect ratio of 4:3 (1.33:1). The traditional iPhone at 3:2 (1.5:1), the 7" Android tablets at 1.6:1 and the tall 16:9’ish devices. If you want a single background image that works on all shaped devices, it has to be tall enough to cover the tall devices and wide enough to cover the wide devices.
If you use the in-the-middle 4:3 as your base, like many people do (i.e. 320x480), then the 4:3 at the same scale is 360x480. Then if you think about what is needed for the 16:9’s, to keep the scale the same as the 320x480 size, then you need a 320x570. So to have one image to rule them all: 360x570. Then for larger screens like the iPad 2, iPhone 4, Kindle Fires, etc. you want a bigger image, many people chose to double that to 720x1440. Then for the Retina iPads, and high def android devices, people will double that again to 1440x2880.
But the key thing is a term called “bleed”. Part of the background will be off screen depending on the device, but it will fully fill the screen.