Never put all eggs in one backet.That`s why.
I still afraid that the online wallets i use might be hacked or run away with my bitcoins.
If you are afraid then make some wise moves now.
You can stay away from web wallets or if there's no way you can access other wallet types then just don't store in just one web wallet like you said "never put all eggs in one basket".
Its always good to have multiple wallets to reduce the risks, as if anything goes wrong with your wallet and if you have diversified your coins to different wallets then your coins in other wallets are safe and you won't loose them.