One thing that I'm surprised hasn't been mentioned yet is that implementing Runnable makes your class more flexible.
If you extend thread then the action you're doing is always going to be in a thread. However, if you implement Runnable it doesn't have to be. You can run it in a thread, or pass it to some kind of executor service, or just pass it around as a task within a single threaded application (maybe to be run at a later time, but within the same thread). The options are a lot more open if you just use Runnable than if you bind yourself to Thread.