Insurance. The funds required to compensate unfortunates for losses due to fire, theft, etc., should be raised by taxation. Private companies make sure they extract this much from punters, and then as much extra as they can possibly manage, in an evil and invidious con game.
Banking. Charging interest is un-Islamic, un-Christian, and creates a welfare mentality among investors who think they can get something for nothing. Banks should be run by the state and invest their money in productive ways.
Transport Infrastructure, Communications Infratstructure and Utilities Infrastructure. Experimental evidence is that private individuals and corporations tear these to pieces in an orgy of pillage. While resources will be most efficiently allocated if vast sections of the country are abandoned and the underclass are allowed to rot, the overall decisions about the amount to be invested in these things, and where it should be invested, ought to be the decision of the elected representatives of the people, Holy Roman Emperor, or Great Council of Giant Robots.*
Health. See Arthur Koestler's book 'The Zero and the Infinite'. The value of the individual to themselves is infinite; their value to the community as a whole is close to zero. Thus health is the field where maximum discord can be expected between the interests of the individual and the community, and where the consumer can be expected to behave with maximum irrationality.
Higher and Technical Education. Here, again there is a large divergence between the interests of the individuals (who want to get rich doing nothing) and the community (which will fall to bits if everyone does this). Also, I have good anecdotal evidence that left to their own devices, students are irrational twits.
Oil Companies. Everyone seems to nationalise these, so it must be a good idea.
*: These are currently my three favourite forms of government.
In other news, I disturbingly seem to have slipped to only 92% Clam nature.