After paying it off, I don't trust myself to not run it up - again. So I prefer to close it and move on with my life. Will this hurt my credit score?

It will temporarily. I would not close it. BUT, if you can't trust yourself to not use it, then close it. Better to be safe.

If this is your only account -- don't close it. Cut up the card or freeze it. You always want some kind of credit history.

You're on the right track in your thinking because the less debt you have the better your credit score will be, the only thing you have to keep in mind is that you want to have credit open to you whether you use it or not so don't close the cards that don't charge annual interest rates. Closing your credit accounts is akin to having less credit available which will hurt your score. So yes, go ahead and pay off your debts and then watch your score go up (with myfico score tracker that gives you live updates as they happen) -- then go back and clean up any mistakes on your credit report. In a short amount of time you'll discover a nice boost in your score

It will hurt your credit score if you have had the card for longer than a year. If you have I would suggest keeping it open and maybe just destroying the card.