I would only store as much in an online wallet as you would carry cash in your wallet...
Just like cash - online wallets are very practical - but not 100% safe.
Remember online wallets are NOT REGULATED. They are not like a bank - they do not have auditors or compliance officers etc... In fact they can just be some undergraduate sat in his bedroom.
If you are going to keep more than this - say what you earn in a week/month then do some due-diligence on the company - at least check they are more than a one-man-band and there is some hope they get someone to PEN test them (i.e. an external expert to try to hack them).
1I think we can trust Bitcoin Core much much more then any other private wallets. Because it is opensorce and community supported. – alexey2baranov – 2017-11-02T09:49:46.890