I've actually had a major change in this regard recently. I used to just send random pieces of furniture or clothing I ended up with, because I love my neighbors and want to be nice to them. However I started thinking on the fact that it's been a very, very, VERY long time since I ever got a piece of sloppy furniture in my game, and it's a set I'd really like to complete, so I started looking up ways to help these pieces spawn.
One thread I found explained that most characters have a piece of sloppy or cardboard furniture somewhere in their inventory and they'll eventually get rid of it, but they need to lose their other furniture items first. D'oh, I thought, because this means I've actually been INCREASING their inventories all this time and just making things tougher on myself! The thread recommended sending them junk items that can take up room in their inventory and force them to use furniture items when they're giving something away; this particular thread recommended seashells. Okay, easy enough, I thought. I started collecting seashells and sending them to my neighbors (especially my most recent one, since obviously I wouldn't have messed up his inventory as much). Unfortunately, a few days later I discovered he'd listed one of the seashells for sale in ReTail -- something the thread I'd read said my neighbors couldn't do! D'OH, now I just messed it up even more!!
So, now my plan (or rather, my hope) is to just take any opportunity I can to siphon items away from them. If they give me a time capsule, I don't return it to them. If they ask me for a new piece of furniture, I give them a fish or a bug, since (so far as I know, anyway) those DEFINITELY can't be listed at ReTail. If they invite me over, I always say yes, so I can buy one of their items while I'm there. And of course, it means I'm now sending them nothing in the mail. I might still send letters if I end up with some stationery, but I'm not doing it just to be nice anymore. And to be honest, it feels pretty terrible, because I just want to be nice to my neighbors!!