As far as "adverse possession" goes, it does (rarely) happen, but I've never heard of a case that didn't also involve paying taxes on someone's property prior to claiming it. That's how it works here, anyway. If you maintain, make improvements to, and pay taxes on adjoining property--as well as publishing a public notice in the newspaper--then you may make a claim of adverse possession (which is not to say it will be granted).
We had a notorious case in Arkansas in a development called "Jet City" adjacent to the Air Force base. A local resident (same guy who never "finishes building" his house, so that he won't have to pay property taxes on a residence) realized that many of the Jet City lots were owned by out-of-towners, and that many of those people had moved, or for whatever reason hadn't been getting their property tax bills, which of course, on raw land, were negligible. He began paying the delinquent taxes on the properties, and would occasionally go and mow a lot (maintenance) or throw an old sofa or something on one (improvements). Then he published a notice in the state daily newspaper, announcing that he was "openly, notoriously, and hostilely" claiming adverse possession of all these properties.
He didn't get any of them, but the courts had to consider it seriously, since he'd followed the letter (if not the spirit) of the law.
