Type II Civilizations are civilizations that have control over more than one stellar system, and/or theoretically are able to harness all the power available in a single star (per Dyson).
So, a civilization that employs some form of faster-than-light travel is likely to be considered a Type II Civilization. Some Type II civilizations may not have capability of travelling faster than light but have the ability to harness the power of their star. This form of a Type II civilization were the creators of the Ringworld in Larry Niven's novel of the same name.
Examples of Type II Civilizations
In these examples, the exact power consumption of their entire civilizations is often unknown. They are estimated to be type II based on the scope of their influence and technology. IE, civilizations with faster than light-drives and control over multiple stellar systems.
The following examples are a different type of civilization from the ones previously mentioned. They may not have faster than light travel, or influence over multiple star systems, but have nonetheless advanced technology and have control over the entire energy output of a single star.
- The Morlocks from the novel, The Time Ships (But not the ones from The Time Machine): These Morlocks have built a form of Dyson Sphere around the sun, harnessing all of its energy output.