Tor
There are probably dozens if not hundreds of applications which don't perform DNS lookups over the proxy they're configured to use. Usually because of an oversight by the developer of the app. This is why you can't just blindly install random apps like Google Chrome and expect them to work with Tor. The only browser recommended by the Tor project is Firefox, and even then you have to install a special plugin called TorButton and you probably want to stick Privoxy in the middle.
I expect there are *many* other flaws in the way Chrome would work with Tor, regarding plugins like Flash and Java and anything else which can create Internet traffic.
If you want all apps to be anonymised, then you need to configure the OS to route all outgoing traffic through Tor. Configuring individual apps to do it can lead to leaks. There is plenty of documentation and discussion on how to do this.
If you read the Tor documentation and understand it, and are careful about how you configure and use it, then you can get a decent level of anonymity. Anything less than that, and all bets are off.


