If you store coins in online wallets and if the site disappears in a sudden one day, you will lose everything.
Are you scared?
Online wallet? It all depends on the type of site. Some sites provide you the private keys so that in case you want to use them on a desktop, it can be possible. If you are afraid of losing your money on an online wallet, then it is better to get a desktop or mobile app wallet which are very handy these day with improved user interface.