All the things already mentioned, basic services.
I do understand the problem about waste in the public sector and having worked in it for 30 years I, along with everyone else in a similar position, could come up with endless examples of things we do inefficiently or pay too much for, so that needs tackling. Those of us on the ground are powerless to do this, we just have to do what we are told/follow policies and procedures, even when they make no sense.
Eg a few weeks ago I needed a train ticket. But I couldn't do what a normal person would do and go online, buy the train ticket and claim back the cost. Oh, no. What I did was:
Go online and find the cost/provider of the ticket I wanted
Fill in a form to send to the team PA.
Team PA tries to buy the ticket via the travel agency we have to use
Travel agency refuses to buy the ticket I asked for and suggests a completely useless alternative.
Back and forth between me, travel agency and Team PA a few times.
Eventually travel agency agrees to buy part of the ticket for the outward journey only (I was going away to do a job where we weren't sure how long it would last, so I wanted a flexible ticket, which was available at minimal extra cost because I knew I would be travelling back at off peak times).
Ticket arrives and it's slightly wrong and I can also see we've been charged approximately 20% more than what it would have cost if I'd just bought it straight off the website myself, but it will do.
And then I was able to come back earlier than originally planned so the fixed ticket they wanted me to have would have been completely useless and non-refundable and I just bought my ticket out of the machine at the station.
And breathe...
So what would be good would be essential public services that are provided efficiently and well run and don't strangle the people who work in them in red tape. Do any countries actually manage this?