Should I put a Turbo in my 2009 Honda Civic 4 door?

Would it be worth it?
What are the benefits of having a turbo?
Other than for racing

Sure you can… But remember this, It's a bolt on, The rest of the engine and drivetrain will become a gigantic fireball with you in the car… Don't forget to wear a Kevlar suit… Just sayin'

Need to build a proper motor if you don't want a time bomb. Slapping on a Internet "kit" is recipe for disaster. Also, if you have any kind of warrantee left, it will be voided. Figure $5,000-$10,000 to get a streetable car. Remember, the rest of your car isn't designed for the added power, so you may need to update your brakes, suspension, transmission, etc…

Other than racing? Then why? Spend all that money for a small gain HP.
Worth it, depends on who is spending the money and what is the purpose. That is subjective.
If you are racing high stakes against other Civics, then YES, you might get back the money you spent on it.
If just for kicks, its worth it if you have money to burn. Its just another fancy toy for you.
Those small engines are not designed for high performance. You may get more performance out of it, but it will definitely quickly shorten the life span of that motor.

I wouldn't. You're going to need to change your oil much more often. You're also going to need to build the engine/transmission to be able to handle the extra power, and suspension/steering/wheels to handle the speed. Turbocharging a car correctly is not cheap. Sure you can buy a $500 turbo kit off ebay and "turbo" any car. But don't expect it to stay running for over 2 minutes.