I would immediately put up a fence. If the house does get sold, it will start you out on the right foot with the new neighbor. In the interum, it hopefully will send some sort of message for the current homeowner as to where their property line ends and yours starts.
In the meantime, do you have the name of the people who currently own the house? Try zillow.com. This is a site where you can go to look up real estate values in different towns, and get exact tax amounts for individual properties. It can also provide the name of the person who carries the mortgage. Not all towns in every state are on this site, however. Another site, zabasearch.com, gives you the ability to enter the person's name and search for them. You can enter the state where that person lives and it will pull up their address and phone number, as well as age. If you can track down the current owners, you can attempt to send a letter via registered mail.
All this access to personal info is a bit scary, yes, but in your case these sites may be useful to you. Good luck.

We can get the access to parcel number and owners of the property by searching at our county records office. Perhaps you can too? Or send a registered letter to the owners at that address, they must be getting mail. And yes, I would definitely move to get that swingset moved!

AND put in a fence, good fences make good neighbors for sure! Start out right away by establishing your boundarylines. I know from experience!

Township will not be able to help you out, you will likely have to go through the county's code enforcement agency. (I know, I live in an unincorporated township)

I'm not sure why you're so worried about things that haven't happened yet, or things that someone told you might have happened. Sounds to me like it's pretty peaceful on that side of your property. Your township isn't likely to do anything based on anecdotal hearsay, either.
I can't imagine that there is much you can do to dictate what people can keep where on their property UNTIL it becomes a problem for you.

Like the others said, put up a fence. Or plant a nice big patch of holly in the landing zone of that swingset. They'll only jump in there once.

Getting sued because someone fell onto your property from somewhere else just seems bizarre. Your neighbor should have had a better lawyer. Imagine if a parchuter landed on your lawn and broke his/her ankle. Are you liable for that, too?

Thanks for all the advice.

Like most of you, I think good fences make good neighbors. Although I've never really been a big "fence fan" myself. Having grown up in a rural farmland community ... when I formerly lived in one of those over-over-saturated subdivisions on the outskirts of a major city I worked in, I always felt like I was living in a box even though fences were necessary to keep the peace between the city folk.

I did look up the owners and got their phone number (yes, very scary how much information is out there on the Internet) - and promptly got hung up on after being told "We don't know who you are, if you want to buy the house call the Realtor" [click]. Yes, I was polite - didn't even get to ask about the playset.

As for getting sued - you're liable for just about anything that happens on your property. Reason why I hate sidewalks. What I don't understand about insurance companies is that they'd rather just pay out instead of fight (like Neighbor B's insurance did). Then, of course, jack your premium. I'm reading my local paper this morning and a drunken motorist ran off a local road, went into someone's yard, hit a tree at high speed that was like 30 feet up in the yard, and is now suing the homeowner for medical expenses because he hit the tree. Now *that's* bizarre ...

Anyway - now I have to ask in another forum about fencing options, what's good, what's junk ... any suggestions would help.

Betatest is correct. As a homeowner, you have trememdous liability for anyone who comes onto your property, invited or not. And the incident he mentioned about the neighbor girl breaking her arm and the subsequent lawsuit is most typical; it has ABSOLUTELY nothing to do with the other guy having a better lawyer.
A family member is an attorney who works for an insurance company. You simply cannot believe the stories of people who sue homeowners and the circumstances surrounding the actions that led to the suits. Everything from a guy who climbed his neighbors tree to retrieve his kite and fell from the tree, breaking both legs. Guy did not ask to enter the property to retrieve the kite. Successfully sued neighbor.
Another guy who developed severe burns caused by accessing his neighbors outdoor electrical outlet with his very defective extension cord to power up a kids blow up moon bounce (did not ask permission of said neighbor to use his outlet). Sued his neighbor for medical and pain and suffering. Successfully.
Neighbor who came onto property while owner was on vacation to cut some flowers (she was not friendly with the neighbor, and was not given permission). Fell and broke her ankle, suffering a very bad break. Sued successfully.
These are only some of the stories I have heard. Some are so shocking and nervy your mouth would drop.
Get the fence. Don't wait for something to happen to you. Your neighbors sound odd. Best to just accept that we all have those neighbors, no matter where you live, and in whatever kind of neighborhood. Good fences make good neighbors, yes.

From time to time, I have had issues with others putting "stuff" on my property. In every case, I first contacted the person in question ( Matt. 18:15-17). In a few cases, that ended the problem. Talked with lawyers, law enforcement- all gave non-specific answers. So I figure that if the real estate is mine, and if the "stuff" was mine, I could move the "stuff" when-and-as I pleased without permission from others. But of others can place "stuff" on my property and it can be removed only as they direct, then they have more "rights" on my property than I do. So if the contact does not produce results, I just move the stuff. In some cases, dispose of it. They get angry and bluff, but that is all. Document all of it. Pictures and video help. Prepare for the worst, but most likely that will end the problem. My suggestion: Disassemble the swing set and put the pieces behind their house. Make no comment about it to anyone. I once used a bulldozer to remove the neighbor's chain link fence from my property.

I have been living in my house for over thirty years we have a yard that is separated by a fence that divides my property which is small and a neighbors we are right on top of each other I raised two children here with

no problems because I was considerate to my close neighbors about 8 years ago a family with 4 young kids moves in they put there four piece swing set up against the property line don’t get me wrong I like kids but there noise over welms us in our back yard we’re sitting ducks there is no level of common sense common curtesy toward us it’s all about them there big family I’ve put a lot of money in my home can’t even enjoy my outdoor space I don’t care if there children play but when there’s four and play dates its really bad we live in New York pay a lot of money to live here just got a two thousand dollar increase in taxes I’m going to seek advice from an attorney because they took my quality of life here from my home I’m sorry kids will be kids but it is there parents job to keep them under control my children were my responsibility you can not treat close neighbors like that I’m sick I feel I lost my outdoor space I hope this can be resolved some people would agree or disagree with this but I had young children on a sat or Sunday I could of put them out at 8:00 in the morning I did not they are in back of me they had two young children out on a Sat at 8:15 in the morning woke me up didn’t care dad called me a crazy lady so I let him have it good solved that problem but because young children get up early does that mean we all due we work during the week sometimes we like to sleep in these people are discussing no regard for no one

No more swing set, I suspect. The youngest kid is probably eighteen years old now! lol