Some things which are more or less impossible purely through private enterprise or systems which worked better in the UK when they were socialised:
Socialised healthcare (private companies make more money through charging on a case-by-case basis, they have no authority to levy a national tax, the overheads would be gargantuan which would be unacceptable, corner-cutting would be rife)
Decent railways (here in the UK the railways were privatised - they were being run appallingly by the government and are now being run appallingly in a very slightly different way by corporations: being more expensive, more crowded and costing more to run (largely subsidised, as the railways are not profitable for the companies) but being slightly safer (a big deal!) - the government was probably marginally preferable.). Theoretically, a government run train operator
Roads (roads are almost universally run by the government in pretty much all countries - if they weren't, how would money be made for them? Tolls up the wazoo.)
Emergency services (would you want to pay every time the fire service or the police came to your house when you dialed the emergency services? A corporation running them would need money from somewhere.)
There're more but suffice to say that government run things can work better than corporate run things if they're run well and in the right sector. If not, they don't (see: British Gas, British Telecom etc. etc. when they were government-owned).