In the past, your choices were to either adjust your gradient (either shortening the length it takes from one color to get to the next or making the colors less drastic), or remove it all together and go flat. I really don't like either of those choices, because, as a designer, it's really limiting. Or you could just leave it.
It seems as though these issues are directly tied to the color depths LCD screens can produce (24 bit compared to 16 bit that most LCD screens see). I won't get into details on why certain phones use X depth compared to Y, because it all truthiness, I don't know.
After some digging around the internet, I came across a tool called DepthDither, by Graphest. It's a free plugin for Photoshop that allows you not only to target a specific color depth (and show you on screen how it will look), it gives you three dithering methods to try fixing the banding. I have to say that the results so far in the last 6-12 months I've been using this tool have been amazing.
Original
At 12 bit (and how a lot of phones would render it)
With DepthDithering applied at 100%
Get it now while it's still free. I imagine the more mobile our world becomes, the more this tool will be in high demand.