Any two currencies can be quoted against each other, but the most actively traded cross currency pairs are the euro versus the British pound, or EUR/GBP, and the euro versus the Japanese yen, or EUR/JPY.
In fact, these two pairs are the only cross-rate currency pairs that appear in the top 10 most traded currency pairs.1
The euro is the base currency for the quote if it is included in the pair. If the British pound is included but the euro is not, the pound is the base.
These currencies are actively traded in the interbank spot foreign exchange market, and to some extent in the forward and options markets.