Widgets are a pretty new thing on mobile phones. People seem to like them too, so much that Apple has included a version of them in their own OS.
Copy and paste was also implemented in Android before iOS (note, I am not claiming android was the first mobile OS to implement copy and paste). Interestingly, android's copy and paste is a near carbon copy of how iOS handles copying and pasting. Another interesting fact is that Apple (it may have even been Jobs himself) stated we got copy and paste and it took so long because Apple waited to "do it right".
Let's talk about stores. One might say Apple's AppStore was an innovation of their own. I would argue against that. We had a store, called Installer (jailbreak), way before Apple implemented an Appstore. At the time, Apple seemed to think the future was in web apps, since they were focusing heavily on those.
But honestly, I don;t understand why something has to be completely newly innovated in every way, shape, and form, to be useful? I think both platforms have added various tidbits to the mobile OS world. In my eyes, it is just as impossible to say Android would be what it is today without iOS as it would be to say iOS would be what it is today without Android.