Are the online bitcoin wallets secure?

Is there an online bitcoin wallet never hacked yet?

I'm sure there is. But even if you pick one of them, you're trusting money to yet underregulated/undercontrolled institutions which might misplace your money, be it through incompetence or by design, disappear tomorrow, or, as you say, get hacked, and you will have basically no recourse. There are very good reasons why the traditional banking industry is heavily regulated.

So I'd suggest to not put your trust in any one such wallet, but split your bitcoins among several, so you won't be left out hanging to dry in the rain when one goes down. I'd also suggest a preference for those online wallets under the regulatory domain of a countries that have the legal framework to deal with them (which might be difficult just yet).

Or keep most of your bitcoins in a wallet at home, make regular backups, keep one of them in a secure off site location and only transfer as much bitcoin into an online wallet as you need. Basically, it's the exact opposite of what I'd counsel someone who asked me where he should put is cash to keep it safe.

There are many advantages using online wallet against offline wallet :

• You do not need to download the whole blockchains, which takes tons of GB on your hard disk, each time you want to transfer bitcoins.
• You do not need to transport your wallet everywhere with you. You can transfer your bitcoins from where you want, when you want, just by remembering your password.
• You do not need to update and configure the wallet, which is hard and can take a lot of time for some (more speaking for altcoins here).

Moreover, from the article you linked us, some are centralized cryptocurrency exchanges. It allows customers to instant trades there cryptocoins instead of waiting the confirmations from the blockchain and in the same time, avoid blockchain fees.

The principal disavantage of online wallet is, of course, the security.