There is a (as Paulie says) very stoopid debate about whether the BNP are right or left wing going on in the blogosphere. I've got a very trad lefty view on this, but I also think it's a pretty pointless debate because it's ultimate a dispute about categorisation more than anything else. Anyway...
Iain Dale argues that the Nazis were called "National Socialists" for a reason. I agree, but for entirely different reasons. Even a quick read of the Nazis' actual history would suggest that they used the socialist label more as a marketing tool than an ideology. Famously the Strasserite wing of the party - which did take the socialism bit a little seriously - was pretty much wiped out in the Knight of Long Knives. So personally I think the Nazis' "socialism' was there because it was designed to appeal to a certain cohort of voters, but had little meaning in practice.
Generally we shouldn't read too much into how political parties and movements name themselves. If we did, as other have pointed out, this presumably means that the Liberal Democrats in the UK and Russia share similar views of the world. It also suggests that the Austrian Freedom Party (I'll be coming back to these guys right at the end) are libertarians, and presumably the NuLabor Third Way shares common ground with that articulated by some of the BNP's hangers on. (Actually there's a great line from Orwell where he talks about the mistakenly literal use of political labels. He's specifically talking about anarchism and he says "us[ing] 'Anarchism' indifferently with 'anarchy'... is a hardly more correct use of words than saying that a Conservative is one who makes jam.")
Another point Iain Dale and some Righties make is that the Nazis shared some key policies with the Left - trade tariffs, nationalisation of certain industries etc. That's true, but as Dave Osler has pointed out in practice the implementation was very different. But I would make the broader point that if adherence to these types of policies makes a party "left-wing" then many mainstream political parties of Right and Left have been left-wing. And what about today? Presumably the Tories are currently a bit left-wing because they support nationalisation of certain banks for now. Follow that through and I guess they must revert to being right-wing once they decide it is time for the Govt to sell its stake in the banks. This shows that actually policy positions - even big ones like favouring public ownership of banks - don't tell us everything. The ideas behind the policy matter too.
This also tells us why this is such a stoopid debate. If you define someone's politics by the means that they advocate to achieve their ends then you will end up with one view of how political parties are aligned. If you define them by their objectives then you end up with with an entirely different perspective. Your method of categorisation defines your answer. To me the objectives of political organisations do matter. From my reading of it the Nazis believed that there were inherent differences in the races that meant that society inevitably would be (and should be) stratified. For me that is incompatible with being a lefty, since we view inequalities as very much challengeable. But that's just my system of categorisation.
I had a similar exprience arguing with a bloke whose view was that all 'real' muslims were the fanatical, scary ones, because the soft and cuddly ones hadn't read (or understood) the Koran properly. So all muslims were scary fundamentalists because only scary fundamentalist could be 'proper' muslims. So I couldn't make the point to him that my friends and acquaintances who were muslims weren't fundies, because to him that had no meaning - they couldn't be muslims in the first place. (Another version of this is of course the Trot view of 'communism' as practiced in the USSR etc).
So personally I think trying to 'win' this 'Nazis are lefties' debate is pointless because ultimately no side has an obligation to accept the any other's taxonomy. And if we don't share the same categorisation system inevitably we will end up with different answers from the same info. And of course each side picks the catergorisation system that is most accurate, and it's just a fluke that the system adopted by the Right defines the Nazis as lefties and vice versa...
PS. In practical terms the the overlap of membership has always been between the BNP (or NF before them) and the Tories, not Labour. When they have been in a position to take power, whether in Germany in the 30s, in Italy up to the present day, or Austria in 2000, fascists and their offspring have repeated allied with the Right, not Left. If fascists are really lefties this alignment is puzzling innit?