With nearly two-thirds of mobile users going online with their cell phones (according to the latest data from Pew Research) ignoring how your web site looks in an iPhone or Android phone is no longer an option.
If your site isn't fully mobile-aware, it's time for a refresh. Make sure your new design uses fluid grids, flexible images, and applies CSS rules based on the dimensions of the user's browser.
Of course, there's more to it than that. Fortunately the folks at WhoIsHostingThis? did some research, and summarized their results in this infographic. It should be enough to get you started on the right foot.