Personally I think just about every developed country should be self-sufficient or form a symbiotic relationship with another country. The way that most developed countries rely on China and Japan (not that I have anything against them) simply promotes instability.
And that's one of the reasons why the EU is so important. The wider our interior market is, the more the EU can become somewhat independent.
For the Brits, the EU isn't quite as convenient as for mainland Europeans, where Schengen et. al mean you can live in one country, and work in another, while conducting business in a third, all without any of the bureaucracy that is needed to normally handle that kind of thing.
The EU introduces a lot of bureaucracy, but it also removes some, by making binding decisions for all member states. This means that each member state does not have to assign quite as many resources to an issue, if a European guideline exists.
Also, interoperability/compatibility is important, and still not completely obtained. I'd really like to see a European tax system, so that businesses can no longer exploit tax havens, while doing business all over Europe. Luxembourg and Ireland come to mind.
The real challenge with regards to the EU, is how to balance the "world government" tendencies with the need for local independence and flexibility. On the other hand, how this can be done is seen in many non-centralist countries, like Germany and the US, where many levels of government exist, with separate competencies and obligations. Extending this to another level should be feasible, if people weren't so afraid of the new.
One of the worst things happening currently on the EU level is that many people feel like they are governed by an entitity they have no control over. This is shamelessly exploited by national governments, to pass unpopular measures, simply be passing them on the European level, where it's "not their fault", and then implementing them locally. In fact of course, the national governments are in many ways involved in the process of European legislation, as are the MEPs, which are directly elected. One of the major issues is probably a lack of reporting on the EU legislative. National debates and politics are often televised, and reported on, but on the European level such reports are rare, and it seems to be enough to complain about absenteeism and otherwise shed a negative light on the EU.
Lack of media attention also means that whichever level of transparency exists (and the EU is probably more transparent than national governments) is not worth a dime, as the fact that anything important is being discussed is often not disseminated, until the final vote has passed.
The EU is mostly a media disaster, in my eyes.