The argument familiar to libertarians is that, because fascism is collectivist, it should be considered left-wing. This is often traced back to Erik von Kuehnelt-Leddihn, and has been brought up recently by Jonah Goldberg in his book. There is also the fact that the originators of fascism were on the left first.
There is a summary of some recent discussion among British libertarian bloggers at the curiously-named don't set fire to your jacket .
John Gray argues in his book Black Mass, which, as promised, I will review here shortly, that fascism, if not actually of the left, is at least a product the same enlightenment mythology, as he sees it. In this he is closely following Kuehnelt-Leddihn.
Mencius at UR has argued the contrary.
In the 1930s, there was no confusion at all as to whether the fascist movements were parties of the extreme Right or of the extreme Left. Everyone agreed. They were parties of the Right. Populist right-wingers to be sure, but right-wingers nonetheless. For once, the conventional wisdom is perfectly accurate.In this case I would go along with him. This is not really a question which has a right or wrong answer, but I think its more useful to classify fascism as right-wing than left-wing. The reason is in what I consider the essence of government, as I wrote yesterday. Politics is not primarily about how society should be governed. It is primarily about who does the governing. So the similarity in policy between far-left and far-right is interesting and noteworthy, but it does not mean they are the same. Politics is primarily about what group should rule, and fascism and communism represent different groups. The left seeks to dispossess the rich; the right seeks to control them. The fact that, after gaining control of the economy, they would each do much the same thing with it, is not enough to make them allies. Since they will always oppose each other, it is not useful to classify them as on the same side.
One reason some libertarians dislike describing fascists as right-wing is that they consider themselves of the right. I think that is a mistake, caused by the history of the cold war, where they sided with the true right against communism. That is all over now, but the personal and organisational ties survive to an extent. Let the fascists have the "right-wing" label; our position is not left or right, but fundamentally "anti-politics". That should have public appeal currently, although it is an admission that we cannot really win the game, because we are not really playing.
Update: I've written a lot more on fascism recently; see here and here.