I've used Instawallet and Flexcoin. Instawallet is very easy to use because you don't need a login name and password. You visit https://www.instawallet.org and it simply gives you a unique and hard-to-guess web address to a bitcoin wallet which you can bookmark. I used this site together with BitPay app for Android, trading a few bitcoins in a diner.
The site has been around since April, 2011. The operator is visible in the bitcointalk forums and responsive enough to emails from users. He is also known to be the developer of the well-known site bitcoinmonitor.com.
http://www.flexcoin.com is also easy, but you need to create an account with username and password to use it. You enjoy the benefits of instant transfer of bitcoins and simple addresses if you deal with other Flexcoin accounts. You pay a small fee when you send bitcoins outside of Flexcoin and earn interest or "discount payments" if you keep a balance in your account. This "bitcoin bank", the first of its kind, is backed by a business company.
Ever since the MyBitcoin incident where thousands of bitcoins were lost, users naturally have become more wary of third-party wallet services. There is hardly any insurance against bitcoin losses and no guarantee of continued service. However, the visibility, responsiveness and reputation of the operators and legitimate business backing, not to mention the security measures, of the service can be good signs to watch out for if you will use online wallet services.