Most of the time in the world of cryptocurrency you are your own bank. Exchanges are places where you should purchase and sell crypto, not a place for you to store your funds.
Places like coinbase (not even their new vault) Binance and Bittrex, are not places you should be keeping your long term holdings. Moving your crypto to offline or paper wallets is the best way to ensure that your money is safe.
When taking you coins offline or putting them into a paper wallet always be sure to write down your secret key and put into safe storage. Laminate the keys and put into a fireproof box. Your secret key is what you need to unlock your fortune.
Many coins have a specific wallet that can be used, but for those who don't there are other options as well.
One popular option is a Ledger Wallet as shown below: 
This device hold your private key for you (as opposed to writing it down on paper and laminating it). When you first open you will be asked to write down a list of words. These words (should you lose / damage your Ledger Wallet) will allow you to retrieve your private key.
They offer wallets for the following:
- BTC
- BCH
- BTG
- EHT
- ETC
- LTC
- DOGE
- ZEC
- XRP
- DASH
- STRAT
- KMD
- ARK
- EXP
- UBQ
- VTC
- VIA
- NEO
- XST
- XLM
- HSR
- DGB
- QTUM
- PIVX
Coins that are built off the Etherum blockchain (ERC20 Token) are able to be put onto myetherwallet.com. That is a great and easy way to put your coins on a paper wallet.
Every coin can somehow be taken offline, and if you are holding long term make sure they are in proper storage.
Do your research and make sure that your holdings are safe!
Note: The information above is intended to enable investors to understand some storage options. It is not intended as and does not constitute investment advice.