(Here's a "reprint" of my answer to this question from another thread, which I am including for reference in case anyone else gets this kind of problem.)
Hey H2524, we're beekeepers and I wanted to chime in here.
First of all, it's really inconsiderate of your neighbour to keep hives so close to your boundary that they interfere with your use of your own property. It may or may not be illegal depending on your local legislation, so check. Either way, can you complain to your town bureaucracies because of nuisance? Also another thing - check with your department of agriculture. In many countries you have to have a license to keep bees and hives need to get inspected on a regular basis for disease and mismanagement. If your neighbour wasn't licensed in a place where licenses are required, they could be fined and/or the bees taken off them. You can basically ask at your department of agriculture about nuisance beehives and whether they have a beekeeper register and can deal with it.
I wouldn't be surprised if they weren't licensed. I say that because part of proper bee management is to re-queen the hives with specially bred gentle queens every 12-24 months because otherwise hives re-queen themselves with increasingly aggressive queens (and therefore produce more aggressive workers) because of interbreeding with feral drones.
We have four hives in our orchard, next to the area that contains my horse tie rail, and have not had any issue with bees bothering us. I also often hang washing on lines in the orchard and don't get bothered unless I'm really close (within 3m) to a hive that hasn't been re-queened in a while. I've only been attacked once by a bee when not actually taking the hives apart, and that was a freak event, I think I must have accidentally partly squashed it or something when watering my vegetables, and boy did it go for me then, you should have seen me run! Got stung right on the rim of a nostril and my nose looked like a potato the next day. The bee pursued me stingless (they lose the sting immediately they sting you, and it dooms them to death because it tears up their abdomen) for another 400 metres and I was still running even though I knew this fact, because of the pain and because I wasn't sure if the original bee had any friends with her! Anyway, never another problem, just a one-off there.
It's not good to keep bee hives close to areas where horses are paddocked, because horses close to hives can get attacked, especially if they are sweating. That's why we have the hives near the utility area where I tie the horses when I'm working with them, and not right next to their actual paddocks. This way I will know if a problem is developing, stop a horse getting into trouble, and make a mental note to re-queen ASAP - which is what I would do if I suddenly got bothered by my bees.
Moving bee hives: The hive entrances have to be plugged up after dark when all the bees are "home" and then the hive has to be moved at least 2km to stop all the workers returning to the original hive position. The other alternative is to move the hive 1-2 m each evening until it is far enough away. You can't do that obviously, but if your neighbours won't, and you have no luck with your authorities, and there is no other way to stop this unacceptable situation then you can bait the bees on your side of the fence with a product called Ant-Rid (sugary liquid with borax in it). Place it in drops on a plate close to the target hive on your side of the fence to prevent non-target insects getting killed by the stuff. Stay away for a while because within a hour the bees will be all over the bait in droves and get quite aggressive. Borax isn't particularly toxic to people, so people won't be killed eating whatever trace they stick in the honey bees are making before they die within a day of eating. Repeat the procedure until no more bees.