It's tons of bureaucracy with very little democracy.
The EU has about 33 thousand employees, this is hardly tons of bureaucracy, just UK local government has 2.3 million employees.
Most of that isn't what people think when they hear bureaucracy.
Ed: And there's much of the reason for the bad rep of the EU inside of the EU. The rest (mostly in the UK) is due to Murdoch's personal interests, obviously.
A recent poll in the US shows that 65% of likely U.S voters think that their country is going in the wrong direction (http://www.rasmussenreports.com/public_content/politics/mood...). And that doesn't even speak of the almost 50% of people who don't vote.
What is special about the EU is that national politicians and tabloid media love to use it as a scapegoat for everything that is wrong with our modern globalised world. That is especially true for the UK.
A few examples do show a blatant lack of democracy, though. In France, we had a referendum regarding the new European constitution. We refused it at 60% (not counting abstention, which by the way was relatively low). Then a dozen months later, the same constitution came back (sections were shuffled around, but it was mostly a copy-paste job). No referendum this time. It was submitted to the parliament instead. They said yes, despite indisputable evidence that the people did not want this. This is as undemocratic as it gets.
Elections don't make a country democratic. We need much stronger guarantees.
The problem was holding the referendum in the first place. Direct democracy does not work because it's a recipe for paralysis.
It's much easier to form a consensus when your constituents are all affluent. It's much easier to govern a small country than a big one.
Switzerland clearly works moderately well, but the barrier for success was far lower than for France.
Then what about making small countries? We could then federate the result. Let the small regions take care of what can be handled locally, and let the federation take care about the big stuff (army, foreign policy…).
When the government makes a decision that contradicts the will of the people, it is not democratic. Period. If the people really held the power, that decision wouldn't have been made in the first place.
The way the government was appointed doesn't matter, once you know of its actual decisions. Being democratically elected doesn't magically make all of your decisions democratic! Even if you stick to lawful decisions, I might add. Besides, there are a lot of ways for elected officials to have different interests than the general population.
---
That said, "democratic" does not mean "good". It is quite possible (though unlikely in my personal opinion) that the will of the people was wrong, and that European treaty was a good thing. In which case it was a good thing to go against the will of the people.
Serious. I'm not saying this particular decision was bad. I'm just saying it was undemocratic.
---
One last thing: you say our "democratically elected" parliament had, among other things, a mandate to ratifying European treaties. Only problem was, the entire political class wanted this particular treaty to happen. Very few thought otherwise. And those had other opinions about other subjects that often made them a big no-no for most people (extreme right and extreme left, mostly).
We did not have much choice when we elected our officials. It was like, this guy who wanted the treaty to happen, and that gal who also wanted the treaty to happen, and maybe that crazy fellow who did not want this, but had also a couple insane ideas we did not endorse.
Not to say that everything's great in europe's current state of affair but be careful not to be too influenced by political propaganda. Remember that the political direction of the union is set by the council which comprises the various head of states of the union. It's not like the parliament is this rogue extranational body that unilaterally dictates its will to the members of the EU.