1 happiness in all your cities.
Half their territory and population towards your score.
For capitulation vassals (not sure whether this applies to voluntary vassals, I just don't get many) you can demand resources (IIRC the first resource is guaranteed, after that they can refuse, but you will be at war).
They go to war along with you, though after capitulation this often doesn't matter.
You can have trade routes with them under mercantilism.
You can enter their territory at will, and (I believe) it acts as your own for healing and such, and you can base aircraft in their cities.
Another great reason: if you are going for conquest, and the civ has a city on a far off island, you don't need to divert your attention to capture it.
While they are supposed to increase you maintenance cost, that can be easily offset by not paying maintenance on the vassal's cities (especially overseas).
There may be exceptions for colonies, but not that I know of.
There are also likely things I missed.
Keep in mind most of those advantages are minor and/or situational, so they aren't always the best thing, often a city is much better to hold yourself.