Do not use online wallets as your main wallet, You should always keep your main wallet offline,
Why? Provided that you can export and backup the private keys, wouldn't an online wallet (like blockchain.info/wallet or strongcoin.com) be just as safe?
The issue is that (generally speaking) online wallets keep the private keys on the server. Even if the operator of the site (and all his employees) are trustworthy, if the server is hacked you could stand to lose everything that you have in the online wallet. Online wallets certainly have their place, think of them as mini-Paypals, but would you keep your life's savings in Paypal even if you trusted them? There is a precident as well, two major online wallet services have been hacked, and also Mt.Gox has been compromised once. The more money that they concentrate, the tastier the hack target that they become. What sum that you may have in your personally operated client wallet generally isn't worth the efforts, if they know that you have anything at all. Mind you, some of them have learned their lesson, and have become relatively hard targets, but that doesn't mean it's impossible. It is impossible to steal your bitcoins from your not running, not online and encrypted wallet.dat file.
That said, I don't entirely take my own advice here, as I have the majority of my funds in a BitcoinSpinner account attached to my android cell phone. But the cavet there is that BitcoinSpinner uses a 'split wallet' design that keeps the actual private keys on my cell phone. The risk for me, then, is the loss or destruction of my cell phone/memory card.
Really, the matter comes down to risk versus convience. If your only dealing with a couple hundred dollars worth of bitcoins, and can afford to risk it, then an online wallet service is very fast and convient; like modern banking. Often easier than Paypal. But if you start to accumulate a very large value in that online account, perhaps a more secure 'savings account' is justified. Either way, if something bad happens to the online service and you lose your shirt, don't blame bitcoin.