You should never store Bitcoins in an online account or on an internet connected device. Think of those things as your wallet. You keep a few bucks there but not your net worth. The reason is that a physical wallet can be easily lost or stolen. In a similar fashion, when you keep Bitcoins in an internet connected account, computer, or mobile phone, they can easily be lost or stolen.
Obviously, using unique and difficult to guess passwords as well as two factor authentication will improve the security of your online account or Bitcoin wallet. The most secure method, however, is cold storage.
Cold storage is when your Bitcoins are stored in such a way that they are completely inaccessible to hackers. There are 2 ways to keep Bitcoins in cold storage. One is to transfer the Bitcoins to a Bitcoin wallet that is not connected to the internet. A flash drive could be used for this or an old computer that is not connected to a network. The 2nd way is to transfer the Bitcoins to a paper wallet.
A paper wallet is a piece of paper with a Bitcoin account and private key written on it. If your Bitcoins are stored on a physical paper wallet, the only way to get the Bitcoins is for a thief to physically see the wallet. As long as you keep the wallet hidden, it is completely secure. A paper wallet can also be password protected so that even if the paper wallet is stolen, the thief can not access your funds. You could continue to access your funds as long as you have a copy of the paper wallet.
The easiest way to print a paper wallet is to go to www.bitaddress.org and click on paper wallet and print it. Make sure to make a copy of your wallet. If your paper wallet is lost or destroyed, you will NEVER be able to access your Bitcoins. They will be lost.