There are a few good wallets that don't ever hold your keys (so you better!) that also allow many many currencies. Someone will correct me if I'm wrong, but I've found the most adaptable wallets to be Jaxx for smaller coins and the big big ones, and Coinomi will hold almost everything else that most people buy or trade.

Some coins still don't have enough support or the right setup to be in some wallets so they have their own. I would stay away from freewallet.org stuff though....they don't necessarily give you full control, and they are very slow.

JAXX and COINOMI are worth looking into. I've been using Jaxx for a while now, and they keep adding more support for more coins. Coinomi I don't use much but keep it around for moving things around sometimes. Jaxx can hold Tokens as well BTW....well all Ethereum accounts can unless stated otherwise, you just can't always access them unless either supported by the wallet or on an Ethereum web wallet access site....or MEW.

The main thing is that you have the only access to your keys, and that you know your coins are in your wallet, and not on some server somewhere and just represented in your wallet.