My experience is based on a Father that owned a roof and gutter company, and I cleaned a lot of gutters with/without guards in my youth, not the product itself but my answer is....
They work about as well as @
Sapphireho describes. For the most part it keeps stuff out of your gutters but it doesn't keep stuff off the top of your gutters. If you have a lot of trees, it now piles up on top and needs to be cleaned off which is easier, and sometimes storms will cause it.
Also, a heavy downpour will overrun most of these types of gutter guards, particularly if you have a lot of roof area, or your roof is steep.
Most come with a lifetime warranty that basically covers gutter cleaning if they stop up.
Personally, I have standard gutters on my house, and a company that comes out and cleans them 3 times a year for $100 per trip. My house is 3 stories tall in the front, and I have about 200ft of gutter that gets cleaned. Never have an issue. To add the guards to my house was estimated at $3,000 the one time I had my gutters replaced so the break even point for me would be 10 years.