Because of volume of transaction that take place, there is so much liquidity during the European session that almost any pair can be traded.
Of course it may be best to stick with the majors (EUR/USD, GBP/USD, USD/JPY, and USD/CHF) as these normally have the tightest spreads. Also, it is these pairs that are normally directly influenced by any news reports that come out during the European session.
You can also try the yen crosses (more specifically, EUR/JPY and GBP/JPY)-as these tend to be pretty volatile at this time. Because these are cross pairs, the spreads might be a little wider though. Next up, we have the New York session, a jungle where dreams are made of. Hey, isn that an Alicia keys song????