I have 23 open credit card accounts, and I know people with many more than that. The number of accounts isn't what hurts, it's how many there's balances on, the balances as a percentage of your total limit, and, of course, age.
I wouldn't keep open an account you're not using if there were an annual fee. However, if there is no fee, I don't see a reason to close it. Just use it every 2-3 months to keep it active and reporting (and pay it in full).