The only *true* way of remaining anonymous is to piggyback off of a neighbour's unsecured wireless connection.
Only works sometimes. You're taking a punt that your neighbour isn't recording the MAC addresses of people who do this ...
... or even recording all their traffic, including emails sent in the clear and that sort of thing.
Not sensible, basically. Setting up an unsecured wireless connection as a trap precisely so as to spy on any traffic from anyone daft enough to use it, with a view to committing identity theft, is hardly a new idea.