Care of this post and thread on Pharyngula (mostly thanks to commenter Coluga), and a cursory google from me, a selection of links to octopus-themed political propaganda:

William Jennings Bryan poster (scroll down)

Harper's Weekly cartoon

Nazi depiction of Churchill as octopus

Crude representation of three-headed octopus representing British political parties with commentary at TONMO†

Bill Gates as octopus

Various Arabic anti-terrorism cartoons, including some octopus related

WTO octopus (scroll down)

Globalization octopus

British imperialism octopus

Scientology octopus

Standard Oil octopus

Standard Oil octopus II (scroll down)

Anti-Chinese cartoon from the Bulletin, 1886

The liquor octopus

Octopus Dei

WW2 anti-Japanese cartoon from the US

Japanese cartoon depicting Russia as octopus, 1904

Another WW2 Japan-as-octopus poster, this time Dutch

French WW2 cartoon of octopus Hitler

"England and the Octopus" 1926, book about urban sprawl

The Railroad Monopoly octopus

1870s greenbacker cartoon (scroll down)

Another Oil trust cartoon

Well, you get the drift. Apart from the obvious use of the tentacles as a motif depicting influence or covetousness, and the strangeness of the beast adding an extra layer of demonisation (perhaps we should say octopusation) of racial or national targets, there's also, as the commenter at TONMO mentions, the diagrammatic value of a creature with eight arms that can be labelled with component features of the great evil depicted, generally a set of nefarious isms. Occasionally a drafter will run out of tentacles and have to add another octopus - apparently no-one ever thinks to use a squid or jellyfish. Perhaps there's a memo I'm not familiar with.

† There's a few others in that thread, including some of those above which I thought I'd been terribly clever digging out of the 'net. Ah well.