Should I include this in my college application?

I’ve been writing a book since my junior year and have yet to finish it or publish it for that matter, it’s still a work in progress basically but I was unsure whether or not to include it in my common app under Activities because I feel like some colleges would doubt whether I was telling the truth or disregard it because its not completed. Should I include it in my app? If so should I put it in Activities or some other spot in the Common App?

If it is important to you and a big commitment of your time, yes, include it with Activities. Think of how to describe what writing it means to you in 150 characters… unless it becomes part of your essay, in which case of course you will say more.
Another person could include her knitting or videogame hobbies. Why not?

There is some disagreement on CC about this. IMO if it is something you do in your room without interacting with others then it is a hobby not an EC and should not be on the activity section of your application. It would be fine to note it in an essay if you can work it in. FWIW I don’t think any college admission officer will be swayed by a book you have been writing but that is not published, has not won any type of writing competition, and remains unfinished. But in the end it is your application and your call.