Undoubtedly best mobile wallet is Mycelium. It helps you making most of bitcoin over phones. You can create master seed, export/import keys, create cold storage, even buy/sell bitcoins using third service directly on app. You will also have liberty to choose between four-tier fees system ranging low, normal, medium and high.
Other solution can be Green Address, Electrum for mobile (Android only), etc.
I'll stay use mycelium and never had any problem i just tested this app since 2 weeks ago but until now the apps are good also tried to import a new wallet address from electrum which is easy to import if you import the private keys your phone will pop up bar code scanner which is automatically read your private keys and import to your mycelium other than that there is no other android wallet are safe except for electrum wallet but there are still having issue base in my experience..
I agree that Mycelium is a good wallet, but I have a problem with the fee that
you can't customize. At least you can't completely decide what to use. Electrum is also
a decent one, but it doesn't give you the dollar amount of your holdings, which is somewhat
annoying. Other than that I like it and Mycelium. Blockchain....meh, I'd stay away, because
I do believe you don't own your own private keys. The simple bitcoin wallet for android is a
total mess, the one where it freezes eventually if there are too many inputs, say from a faucet.
That's the most absurd thing ever.