I have a Discover card that I opened two years ago, transferred a balance from another card to take advantage of 0% interest on balance transfers, and paid it off within the 18 month period. It currently sits with a zero balance. Should I keep it open to boost my debt/credit ratio, or close it because I use it for nothing?

A wide open credit card in your travel bag is always a good thing to get you home in an emergency.

I'd keep it for the reason you mentioned... Closing it would hurt your credit report.  Use it every six months to buy a tank of gas to help you remember that you have it if that helps you.

I actually did the opposite. I canceled all of my cards and only pay with cash or my debit card, which works exactly like a credit card. Also, while using a credit card can improve credit it can just as easily hurt it if you miss payments, have too many credit cards, run up high balances or max them out. When I went to buy a home I had terrible credit around 600, I had 4 credit cards, 3 bank account and several money market accounts and CDs. Apparently I had too many accounts for my age and was considered a financial risk lol. Yet I had almost enough cash to buy the home outright. Meanwhile my wife, had about $500 to her name and $50,000 in debt but had a 700+ score

F**k the banks, they get wealthy off the poor and ignorant. If you have a decent job and can save money there is no reason credit card or loans, just save up and buy what you want with cash. And if you don’t have the cash, which means you’re probably trying to live above your means and you shouldn’t be buying it.

You don't get a bad credit score from having too many accounts.  That's generally viewed as a positive.  You had a bad credit score because you had missed a lot of payments or had high balances on your cards.  

Closing accounts with no balance on them is a terrible idea (one I was guilty of before I learned how your credit score works) unless you have terrible self control.  Keep it open.

If nothing else, work the rewards.

I pay all of my bills with a credit card that gives me rewards and purchase protection, then pay it off immediately from my bank account.  Safer than a debit card.

I have an 800+ and whenever I have had my credit report one of the derogatory comments is "too many accounts."  They have to put something on there.  Length of time and balance too high are the other two.  I have a card I don't usually use except every now and then for gas or to order a pizza.  Keeping it won't hurt you.

I already do that...using the Capital One Venture card to save up frequent flyer miles so the wife and I can fly to the Philippines to visit her family someday.

You should always have at least your preferred card and a backup card in case the preferred card gets compromised.
That said, I have a lot of credit card accounts.  Almost all of them are dormant (two are active, 1 for personal, another for joint with my wife).  
It won't hurt my feelings if one gets closed, but I am not actively trying to close them either.