Since EC Regulation 261/2004 is a European law, it applies to EU air space. You do not have to be an EU citizen to claim compensation for delayed flights.
Thus, even if you are a US or non-EU citizen, you can claim for flights departed from any airport located in the EU member states (with any airline) or arrived in the EU (with an EU airline). EU 261 rule is even applicable to Iceland, Norway, and Switzerland.