I've had cats for a long time and I simply don't want them anymore.
Since you are the one who's taking care of them, why do you no longer want them?
I am just getting tired of them being around.
If you can no longer take care of them it is acceptable to give your cats away but to a good home. If it is just for being tired of them, then that is irresponsible. Cats are family, and you need to treat them as so, otherwise you will look bad concerning others.
Oh well. I'll leave them in my neighbor's yard.
That's not a good reason to get rid of your pets, and you shouldn't place them into your neighbor's yard at all. If you really want to get rid of them then you need to make sure that you give them away to someone who will want them and take care of them, or else it is pretty much just animal abuse.