If you use an online wallet you put your entire trust in the service provider. If the service provider is hacked, goes down or, disappears into the night then so does your BTC, permanently. They own all the private keys.
The risk of attack is generally considered to be greater for an online wallet provider than it is for a wallet on a personal PC since online wallets are believed to house so many more BTC's under one roof, although, if their security is good it may be easier to take over one single user's PC sitting at home if their security is not so good but the reward then is usually much lower. Online providers have been hacked and cleaned out more than once in the past.
The same risk applies to online exchanges. You should not keep more balance online than you absolutely need to at any one time.
The most sincere advice I can offer at a personal level is to use a reputable wallet from the official source at http://bitcoin.org/ and choose one that suits your needs.