There are both softwares and hardware wallets that support multiple altcoins at once. You just need to know how to choose the correct for your security needs.
If you want maximum security, buy a hardware wallet. e.g: Ledger Nano S, Trezor
Which altcoins are supported by Ledger:
http://support.ledgerwallet.com/knowledge_base/topics/which-altcoins-are-supported-by-the-nano-s-and-the-blueWhich altcoins are supported by Trezor:
Bitcoin, LTC, ETH (with MyEtherWallet), DASH, Zcash
Or if you don't want to buy a hardware wallet, there are softwares that support multiple altcoins:
Exodus (
https://www.exodus.io/)
They support: Aragon, Augur, Bitcoin, Decred, Dash, EOS, Ethereum, Gnosis, Golem, Litecoin and OmiseGo.
Coinomi for Android (
https://coinomi.com/)
Which coins they support:
https://coinomi.com/#supported-coins
