If your neighbors are married and/or with kids, sign the man of the house up for NAMBLA newsletters, if they're still around.
Every married or live-in couple needs mail order bride catalogs. Try to get a few so they can pick out the most charming waif out of each geographic region.
The freecycle idea is pretty genius, actually. It would be harder with you living in an apartment. You could put a little twist on it and when someone emails you for the arrangement, just ask them to pick it up at "your" next door neighbors. That way, everyone knows apt # 5 (or whatever your annoying neighbors apartment is) is bringing in hordes of creepy people to try to steal their shit. If you get lucky, they may even get evicted.
Any time they make a call to a restaurant, cab, or anything like that, immediately call back and cancel. (this is where call monitoring would be helpful).
If you don't live with anyone else and have adjacent neighbors, I recommend Project Blender.
Contact the Church of Latter Day Saints and let them know you want someone to come over to "your" house for a religious conversation. Find out what day they're coming and make sure they can get in the building.
If you have their phone numbers, call all the video stores in your area and see if they have accounts. If they do, change all the info that you can. If they can't figure the shit out, they'll have to go through the hassle of creating a new account. It's childish, but it can work.
Collect call them endlessly. You'd be amazed how often people accept collect calls, even if they know they're being billed. I'd do this from a payphone, of course. I was able to do this to one person nearly daily for a month before he stopped accepting the charges all the time. After that, he'd still accept them 50% of the time or so. He was probably senile, though, as I was using his own name.