There is a very full series of events in York.  The most important are:

York Races.  Held 6 to 8 times in the year with the key meetings in May and August.

Mystery Plays.  Medieval Passion plays, revived after the Second World War and the forum which first brought Dame Judi Dench to critical attention.  Don't run every year and vary between the traditional plays acted on floats carried around the city and more formal renditions which change venues, last time being staged in the Minster.

York Festival of Food and Drink. Late September every year.  The Food element majors on Yorkshire food, while the drinks program has a world wide and wine orientated theme.  The range of events is very wide with demonstrations, tastings, markets and dinners everyday for 10 days.  Big 'Slow Food' / Fairtrade and other 'worthy' food element allied with lots of hands on cooking for kids.

Viking Festival, February.  A big event with a lots of appeal for children - lots of dressing up and mock fighting but backed with the serious educational purpose of the Viking Centre.

York Early Music Festival.  Early July.  World class event with very serious intent.

St Nicholas Fair and other pre Christmas events.  A bit of a mix bag with some very high quality music associated with the Minster and Early Music Center.  Unfortunately the market at St Nicholas fair (late November) isn't on a par with the Food Festival, but there is a good spin off event, Festival of the Angels at around the same time.