Tasmanians are looked down upon and mocked by the rest of Australia much in the same way that Alabama or Newfoundland are in their respective countries. They're stereotyped as slow, backwards, hickish, and hopelessly inbred.
Tasmania was the site of the worst shooting spree in Australia's history, the Port Arthur Massacre. This shooting was the catalyst for Prime Minister John Howard's government instituting a range of new, tougher gun laws. Until a few years ago, being homosexual was illegal in Tasmania, while owning an AK-47 wasn't.
Tasmania is something of a world apart - a barely acknowledged part of Australia... at the Perth Commonwealth Games a map of Australia in the opening festivities left Tasmania out. And, of course, quite a few foreigners seem to think the place is a separate country.
That said, none of this is really true and it's just a vaguely overlooked part of the same country that gets made fun of. While stereotyped as backwards, Tasmania has now (scant years after decriminalising sodomy passed some of the most progressive gay rights legislation in the world - certainly the most progressive in John Howard's Australia.
Tasmania is one of the two Australian states that I've never visited, and the few Tasmanians that I've met have been exceedingly nice people. Except for this one arsehole, but he hadn't lived in Tasmania for quite a few years...