In my general socialist dream, all boring things should be non profit - education, healthcare, food (agriculture side, not th end product), water, electricity, land, communincations, transport (railway, busses), etc… Basically things where 2 people doing someething will likely not breed creativity, but only trying to beat the other will require doing things like advertising, and to maintain profits, you would have to cost cut. these things also happen to be necessities that everyone has, and so must be provided by govt, and covered by taxes.

as for examples, atleast in us (and a lot of world), most governments do not operate telecoms (the cellular service), even though it is a boring thing. in india (where i live), there is bsnl and mtnl, and pprovides a basic service, which not only keeps the for profit companies at their toes (technically they are not non-profit, at least not registered one, but they basically do not aim to make profits). another example is agriculture - it is often subsidised, and but it is still for profit. over here, we have large cooperatives (they are also not non profits, and they actually do make profits - thy just invest back into the cooperative) for dairy and agri industry, which not only helps farmers havee stable incomes, but they can often fall back on their saved profits. railways are often partly (or completely) govt owned (might not be the case in land of free, but i know of amtrak) so that is already a well known example - try to use all profits to maintain rail cars and tracks.

beyond these, things can be for profit (art or media for example), where 2 separate things can exist, do not (necessarily) eat each others business and often done for leisurely needs (not necessities)