Interesting that no one has mentioned Google Keep - it works for me, mostly because it's available for both Android and IOS and as a web service. I have to admit syncing is not always perfect, though.
Just curious, any particular reason why others don't mention it?
I use Keep, and it's become a pretty central part of my life over the last year or so. I never stuck with any other to-do apps- either they were way too extensive (Evernote) or not flexible enough (Wanderlist, Google tasks, Any.do, etc). I like Keep because it lets me store random notes that I need access to during the year (books I want to read, workout lists), to do lists that are transient (a shopping list, recipes), and to do lists that need to stick around for a while (Personal Goals for September). Something about having all that just displayed on one scrollable screen works really well with my mindset where other apps feel tedious and unhelpful.