The Slippery Slope is the fallacy of deriving a series of increasingly unacceptable consequences.
The Slippery Slope is commonly employed by both conservatives and libertarians to argue that a certain policy will result in the country becoming communist or anarchist respectively. For example, on the issue of gun control, a European conservative may argue that if non-automatic guns are legalised, soon automatic guns will be legalised, and then all weapons will be legalised, the police and military will no longer be able to maintain control and society will descend into anarchy. An American libertarian may argue that if laws are passed against fully-automatic guns, soon all guns will be banned, then other weapons, and then other rights will be restricted and the country will become a communist state.
To show the fallacy has occured, show that the final event need not occur as a result of the first event. Alternatively, argue that one particular link in the chain is invalid. In the first example above, we can argue that legalising non-automatic guns (for defence or for pest control) need not lead to the legalisation of automatic guns (as they are not necessary for personal defence or pest control). In the second example above, we can argue that most European countries have banned fully-automatic guns, but are clearly not communist states.
The Slippery Slope is a special case of The False Dilemma - it assumes you must either reject the first proposition, or accept the final consequence.