Only 5 countries in the EEA (3 also being in the EU) don't have national ID cards: Denmark, Iceland (which does actually have one, but it doesn't state nationality so it can't be used as ID outside of the nordic union), Ireland, Norway and the UK (abolished in 2010 following their 2006 introduction). Those do have to use passports for free movement (and to enter countries like Albania which offer general entry on the sole basis of EEA citizenship).
Both Ireland and Norway have decided to start issuing national ID cards soon (2015 and 2017 respectively).
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