Every city in Catholic/Anglican European countries has a cathedral (+ sometimes additional cathedral-size basilicas). Most of them are fairly empty during the mass though.
There are too many cathedrals to recommend for sightseeing in Europe.
In the UK, the best are St Paul Cathedral in London (Neo-classical), Westminster Abbey in London (Gothic), Salisbury Cathedral (Gothic) and Lincoln Cathedral (Gothic).
In Belgium, go for St Michael & Gudula Cathedral in Brussels (Gothic), the Basilica of Koekelberg in Brussels (weird mix of neo-gothic and art-deco), Mechelen Cathedral (97m high tower; gothic), Tournai Cathedral (Romanesque with 5 towers in UNESCO World Heritage), St Bavo in Ghent (Gothic) and Our Lady's Cathedral in Antwerp (Gothic).
In France, the most impressive are Rheims, Chartres, Paris, Amiens and Bourges (all Gothic).
In Italy, naturally St Peter of Rome, the Duomo of Florence, the Duomo of Milano, San Marco in Venice, but also the Duomi of Siena, Pisa and Arezzo, the Basilica di Superga in Turin, and the Cathedral of Palermo.
In Germany, the best is the Cathedral of Cologne (Gothic), but there are many other nice Baroque ones.
In Spain, don't miss the cathedral of Sevilla, the mosque-converted-in-cathedral of Cordoba, Santiago de Compostela, and the Gothic cathedral of Leon, Burgos, Salamanca... Not a cathedral but as big, the Gaudi's art-nouveau Sagrada Familia in Barcelona is one of Europe's most famous.