Anyone using a 3rd party wallet host will get all their coins stolen, confiscated, or magically disappeared at some point. Nobody should use them, ever. It's safer, faster, and infinitely smarter to secure your own wallet file yourself.
They only host an encrypted wallet that is decrypted in the browser. They do not store any bitcoins.
There is no difference in me using this service than using the official client - except it is much more functional and can be accessed from any computer.
The same vigilance is necessary (key loggers etc) but blockchain wallet is worlds apart from the mybitcoin like websites that you have to trust to hold bitcoins for you.
You remain in control - you hold all the private keys.
How is using a browser interface any different than using a stand alone piece of software? - it's just a program running in the browser. You can even use it offline.
It's open source and you can examine the code:
https://github.com/blockchain