A government's role should be: (pick one)
1. Break up monopolies, reduce barriers to market entry, and encourage competition, or
2. Regulate the behavior of monopolies.
Net Neutrality attempts to do #2.
3. All of the above.
Natural monopolies should be regulated. This includes utilities (power, water, telephone) that rely on physical infrastructure. The owner of the infrastructure (the cables, the pipes), should be strictly regulated - and where possible being forced to allow competitors on their infrastructure. Ideally, owners of infrastructure and service providers using that infrastructure are separate.
The most obvious and easy to understand example is roads. The government builds roads and bridges, and everyone can use those roads and bridges - either for free, or against a fixed cost which is the same for everyone. Every driver pays the same toll to cross a bridge, based only on things like size/weight/type of the vehicle and maybe the time of the day, regardless of which company he works for. It's the same for everyone, roads are neutral.
In Europe, this has gone so far as to decouple rail roads from rail transport providers, power lines from power suppliers, telephone lines from telephone/ADSL Internet suppliers, etc. I'll be the first to admit that it doesn't always go smooth and there are issues, but the idea is the correct one. It's just really hard to execute well. Net neutrality is also an issue there, though generally the governments are highly in favour of net neutrality, and in the end we'll have full separation between providers of physical infrastructure (the cables in the ground), network service providers (the ISPs providing connectivity), and content providers (the individual web sites).
That'd be the ideal situation.
Low barrier of entry to the content market (everyone can set up a web site and be sure that all their potential customers can actually reach that site on equal footing with all other sites) which of course enhances competition. Low barrier of entry to the service provider market, as everyone can rent the required connectivity for a fixed, known price.
Physical infrastructure is a natural monopoly, very high barrier of entry, and therefore has to be highly regulated. This is something that I consider a prime government task, be it done directly, through a SOE, by appointing a commercial entity to do it, or even by forcing a commercial entity to open up their existing networks to the competition.