If you store coins in online wallets and if the site disappears in a sudden one day, you will lose everything.
Are you scared?
You mean exchanges? Because there are a few wallets which dont gave you a private key, other are giving you a private key when you register to them, so if they dissapear, you can go to another wallet, export private key and get acess to your wallet. Online wallet is just a shell, your funds storing in blockchain, not in online wallet.