I've tried a few and none of them worked very well. The latest I've seen is the very fine stainless steel screen. My neighbor sells them here in Florida.
My house has ONE SINGLE GUTTER, by the pool, and believe me, that's more than enough to irritate me.
If I would give anyone advice, it would be to eliminate gutters entirely. This is possible here in Florida because of the sandy soil, and no mud to splash onto the house. The soil also drains almost immediately due to the sand.
There are ways to do this up north too of course, such as stone covered surfaces at the ground level (with drainage). I've even seen concrete poured right up to the foundation for runoff, if the water has a place to go.
Those downspouts going into the ground will eventually plug up too. They need to be surface drains IMO.