Personally making use of MyCelium on Android (No iOS app yet). The new HD version was released this past week.

Tried many others but settled on MyCelium as I like what it offers.

In regards to safety..... They all say their wallets are safe and maybe they are. I would however have sleepless nights with all my coins lying in a phone wallet. I never keep more than around 0.5 in my phone wallet. Rest is kept offline and moved to the phone as required.