You might have some success with talking to them, or even dropping a leaflet or a print out in their mailbox explaining the problem and encouraging them to check their yard for breeding grounds. A lot of folks (especially young ones) just don't think about that kind of thing, but very few people actually like mosquitos, so a polite reminder every couple years or when someone new moves in might do some good.
I had a neighbor with a bunch of trash in his backyard that collected water causing mosquito breeding. It was impossible to be outside for more than a few minutes. Despite being friendly with him, he took offense when I pointed out his problem and even offered to help lug the trash to the curb with him. Some people are just too proud.
