There are some nice and simple to do list apps (eg. Notally on Android) that have no syncing. Then there are some platform specific solutions (eg. the Apple's Notes app) that work well on platform.
I've been looking for something just to share a shopping list with my SO, and all I could find were elaborate SaaS productivity suites with projects and deadlines and calendars and project management features, but nothing just for syncing a single to do list between an iPhone and an Android device.