Android/iOS/Web: It's advisable to separate your email from your to-do list and some productivity hackers are all for keeping separate apps for each purpose, like lists, notes, tasks and more. But if you want that "one app to rule them all" for productivity, IQTELL does a great job.
Available for free on the Web, Android and iOS, this app does it all. It will fetch email from different services and make it available in an interface similar to Gmail. It lets you create to-do lists and action items. You can tag everything, as well as create larger projects. When you set deadlines, it will show you what's due today or what's overdue. And there's a neat "Waiting For" category to list things you are waiting to happen and satisfyingly cross them off as they do.
Everything's stored in the cloud so it's backed up and you can retrieve it later. Plus, IQTELL has a universal search tool, letting you search in your email, notes, to-do lists and other items from one place.