What you're bringing
Iceland's rules are not EU rules
Iceland isn't in the EU. Travellers arriving from outside Iceland (including most tourists) get a duty-free allowance of 1 litre of spirits (over 22% ABV) + 2 litres of wine + 6 litres of beer for personal use. Tobacco allowance is 200 cigarettes or 250g of other tobacco products. There is also a generic ISK 125,000 "other goods" allowance.
For 18–19 year-olds the alcohol allowance is reduced. Beer/wine at 18, but spirits at 20. Anything over the allowance is taxed heavily (customs duty + VAT) and must be declared at the red channel. Alcohol is famously expensive in Iceland for a reason — buying more than the allowance and paying duty is sometimes still cheaper than buying at the state-run Vínbúðin store.
FAQ
Can I bring duty-free from KEF on arrival?
Yes — but only if you're leaving Iceland and entering another country. The duty-free shop at KEF is for departing passengers. On arrival, you can only bring in the personal-use allowance above.
Is the alcohol cheaper at Vínbúðin?
Vínbúðin is the state liquor store. Beer at Vínbúðin is reasonable (~ISK 350–500 for a 500ml can); wine and spirits are very expensive. Bring what you can within the allowance.
What about beer in restaurants?
ISK 1,400–2,200 for a 0.5L pint — much cheaper than wine. Local microbreweries (Borg, Æðar) are excellent and worth trying at least once.