My favorite Bitcoin wallet is Electrum—it's simple to use but has so many awesome features other wallets miss out on. For example, with Electrum, you can update the fee on transactions you send out with a fee that's too low. You can even have wallets with two-factor authentication (2FA) making it more secure.

My favorite altcoin wallet is Jaxx, because it has Shapeshift (exchange) built in between coins and supports a huge amount of coins.