Most gutter covers or gutter screens are designed to limit the number of gutter cleanings you need, not eliminate them. There are over 100 different types of gutter covers currently sold on the market today. Some are solid covers and some are perforate covers like a screen, but they all need some kind of maintenance.
A screened gutter is just that: a screen. They are designed to filter out the big leaves and debris that would otherwise cause the gutter to clog and overflow. However, they still let through the little stuff which can cause sludge to build up on the bottom of the gutter. That sludge will rot out the gutter or create a dam, causing the water to backup and overflow. For these reasons, the gutter still needs to be cleaned, just not as often.
Gutters that have no covers, “open gutters,” should be cleaned a minimum of two times a year, but may even need to be cleaned three or four times a year, depending on the number of trees you have and how close they are to your house. A gutter with a screen cover on it will need to be cleaned once a year every spring. “April showers bring May flowers, which bring June gutter cleanings.”