I know there are many wallets for Android and IOS which is easy to use and safe. Coinomi is a good choice for Android users. This is just my personal choice and I wanted to know which wallet do you use on your mobile, why?
Coinomi is the best altcoin wallet. Coinomi supports many altcoins that no other wallet does. It has a build in exchange too.
Supported Coins (132!!):
Sorry I can't list all the names of the coin, go here to see the list
https://coinomi.com/#supported-coins Here is a screenshot of the beginning of the list:

Most major coins are on the list.
Wallet type: Cold storage, encrypted
Android: Yes
iOS: Yes - Beta mode
Built-in exchange: Yes
Ease of use: Very easy, lightweight
Safety: Very Good
Open source: Yes
Website:
https://coinomi.comSource:
https://coinomi.comI have heard from many people about exodus wallet. It has multiple crypto currencies and is one of the most secure desktop wallet for storing crypto currencies. The look is quite good and it operates pretty smooth. The private keys are also not exposed. I have heard quite much about coinomi too. It also has an inbuilt exchange and support pretty many coins.
Coinomi is also known to support many forks that occur. So I guess coinomi is also pretty great. By the way I use coinpayments. It is also a good wallet and has additional feature of vault to secure your funds, so they are not lost during attack or are not hacked.