I don't know about how many accounts you should have open with 0 balances, but I do know that maintaining a zero balance isn't necessarily good. You need to show you can manage credit wisely. Unfortunately, that means maintaining LOW balances. I've been told keeping your util on the CC's to under 10% is great. Under 7% is better.
Sadly, that means on a $300 limit card, you should keep a revolving balance of around $20 or so. Charge, pay, charge, pay.... it's a merry-go-round!