do not use online wallets and certainly do not use an exchange site for storing any coins not only litecoin because of the risks these methods have.
Whilst using online wallets are generally not recommended for long term storage of Litecoin, it would be preferable for people to use
litevault.net. LiteVault was built by a well known LTC enthusiast, and coblee has personally vouched for the usage of the site.
LiteVault doesn't have access to any of your coins, and can only see an AES cipher of your private key. When you log in, your password deciphers the private key. Everything else is done within your browser (through bitcoin-js).