The EU's own statement at http://europa.eu.int/inst-en.htm#commission: "The role and responsibilities of the European Commission place it firmly at the heart of the European Union's policy-making process. In some respects, it acts as the heart of Europe, from which the other institutions derive much of their energy and purpose."

Members
The EC does have 20 members: two from the larger countries France, Germany, Italy, Spain and the United Kingdom and one from each of the other (smaller) Member States. The Member State government appoints a commisioner and the European Parliament (EP) votes for approval. Each member "is obliged to be completely independent of their national governments and to act only in the interests of the European Union". But completely independent isn't possible in reality: often the appointed commissioner served some time for a specific government, and especially their political party (I'd be surprised when e.g. a liberal government would prefer to send a delegate who was an active member of the Green Party). Further, the ones who appointed the commissioner(s) certainly would appreciate a sign that the commissioner thanks them for appointing him/her.
The Commission is supported by 23 Directorates-General and 9 administrative services (on another EU-site (http://europa.eu.int/comm/dgs_en.htm) I've counted 35 of those groups though), all together more than 16000 staff members (of which about one fifth for translations and interpretations)

Activities
  • Initiate proposals for legislation; with their proposal they have to judge in accordance what is best for the Union and its citizens as a whole. They better do! However, it is easier said than done in situations that can be beneficiary for a few countries, but with detrimental] effects for others, and where the few countries that gain from it do have the majority of the votes. (Or vice versa of course.) On almost all topics the EC does have the exclusive right on initiative, except the fields of common foreign and security policy and cooperation in the fields of justice and home affairs; but in that case, the EC participates in discussions at all levels.
  • Guardian of the Treaties and execute EU policies and actions; making sure that the legislation is allpied correctly (also for each case defining what "correctly" means in the specific context). If individuals, firms or organisations violate the regulations, they can be fined or brought to the Court of Justice (extreme scenario), for example in cases of illegal price-fixing and market-rigging cartels. In most of the cases a "serious warning" with a deadline to solve the situation is enough, because those warnings concerning cartels do get a lot of media attention in the EU Member States and/or the specific country.
  • Besides the above-mentioned responsibilities, they're allowed to do even more: the EC manages the EU budget (in cooperation with the European Court of Auditors). They think that the "EU’s effectiveness in the world is enhanced by the Commission’s role as negotiator of trade and cooperation agreements with other countries or groups of countries". An example of this is their involvement during the GATT negotiations.
There are plans to modernize the EC and the surrounding structure, but the statements made are quite vague, with lots of openings for your own interpretation. It seems that their aim is to narrow (or even close?) the increasing gap between the EP and the Member States and streamline their civil service apparatus. Further, the amount of commissioners may change due to expansion of the EU (which may be postponed to 2005) and/or the representatives of the smaller countries may take seat on a rotational basis. Time will tell.

If you want to read more on the EC and their "hot news" etc. check the home page at http://europa.eu.int/comm/index_en.htm

See also European Union and European Parliament