They are safe as long as they are operating, sounds ironic isn't it? lol. Anyways, for much wiser way to deal on any bitcoin web wallets while using them, just use their features or services that can give you comfortability when doing a transaction and NOT as your main storage to store your lovely bitcoins.

No doubt that most of the bitcoin web wallets have unique characteristics that can their user a hassle free transactions whether to buy and to sell bitcoin. If by any case that you only have to use an online wallet to store your bitcoin, sort out all web wallets you known and research if they are a registered company. Not an assurance that it was a safe one but it's more wiser if you will use a service of a registered one that doesn't have an anonymous owners and staffs.