I have an 06 Honda Shadow Spirit VT1100c with 18000 miles. I noticed that it was running like it was cold at low speeds and seemed to be a little rough at highway speeds. I then noticed that it had an exhaust leak at the cylinder and was told this was why it was running badly. So I changed the exhaust gaskets and while doing this I notice the back cylinder was really black and the front appeared clean same was noticed at the ends of the pipes. It does seem to be running better with a little bit more throttle responsiveness (maybe my imagination). What would cause the build up of carbon and if it was the exhaust leak will it clean its self out?

Yes the exhaust leak could have caused the build up and if it is running correctly now should blow that out in a bit.

One other thing I would check is for a leak on the intake - where the carb or FI connects to the cylinder. This could cause the same symptoms and build up.

Exhaust leak would definitely cause the black carbon build up you see. Short of opening the top of the motor, the best thing you can do is take it for some long open rides to blow some of that out.

You can also add some Sea Foam to help clean the carbon build up.