We still don't vote for the executive branch.

The executive branch has to be approved by the EU parliament, so technically we do. Just not directly.

The Eurogroup has the same legal status and regulations as a bunch of guys doing a meeting on a pub, yet, important decisions are made in the Eurogroup. Because of the Eurogroup having no law or regulation, you might be part of the EU but not get invited (ask Varoufakis/Greece).

Not after the Lisbon treaty, and they are closely related to the EU Council (the "other" chamber of the parliament) - particularly to the ECOFin (which is the subset of EU council members which adopted the Euro and where the policies are actually voted). Varoufakis left the Eurogroup, anyway, it's not like he was not invited.

That said, I don't like it too. No real transparency or accountability is always bad. And I'm not saying the EU is perfect - far from it! - I'm just saying that where it's not perfect it is because it is a big compromise between people wanting a federation and people wanting to keep their power and an economic union.

The European Commission does whatever it wants and the EU parliament is powerless. The EC is unelected and they have shown countless times that they don't give two hoots about the people. The whole thing is absolutely undemocratic.

The EC president is proposed by the Council (made by governments elected by EU citizens), each member of the EC is nominated by the government of a member state and then the entire EC is approved by the Parliament (elected by the EU citizens). The parliament can also vote the entire EC out of their job with a vote of no-confidence.

How is that undemocratic?

1. Laws are only proposed by EC, not the Parliament (as in parliamentary democracies). 2. EP is only able to vote against them and ammend them. 3. A "no" vote by EP doesn't mean anything. If the Council (i.e. the governments, which in parliamentary democracies don't have the power to make new law) disagrees, a compromise must be seeked. 4. Making a "no" stick in EP requires more than just a majority. Happened once (with the software patents).

How is that democratic?

The system is far from perfect, but the governments are the other chamber of the parliament in the context of the EU, not the executive power, which is the commission (which is nominated by the council, but also voted in by the parliament once again).

The member states themselves (which sorry, democratically speaking means their citizens) want to keep the council more powerful than the parliament. Fixing the power disparity has always been hard, since the member state don't really want to give away their power to the EU.

Anyway, a "no" vote from the EP means a great deal, your information seems outdated to me. The EC can approve a law proposed by the commission alone only in a restricted subset of topics. Everything else is dealt with with the parliament and the council being on equal footing and acting as a bicameral democracy with equal chambers would when approving a law.

The alternative of the current system is to reduce the power the member states hold in the EU creating a real federation or US of Europe. Which for sure will not happen in the short term, and if the EU does not react correctly (and strongly) to this vote, probably never will.

House of Lords.

How is that democratic?

It suffices to look at how they behaved themselves and continue to behave themselves while trying to shove TTIP down our throats. They are nothing more than a front for corporate lobbyists to write legislation to suit themselves.

As for the EP. 1. It is composed of amateur politicians. 2. They are effectively powerless. 3. They can easily be bought.

If it is composed of amateur politicians (which is not at least in some cases, but I agree in many it has been used as a way to park out politicians that did not get a seat in a national election...) the fault is also with the EU people that always underestimated (look at the turnouts!) how important the institution was, particularly after 2009, when it got more power and control.