The legal jargon states there must be a minimum of 1.6mm tread depth accross 3/4 of the tread width.

Realistically though they need changing before this as wet weather performace reduces as the depth decreaces and when you get down to about 3mm very often manufacturers use a harder compound which is less grippy.

Another thing to note is the tyres age, denoted by the dot number - for instance 4212 is manufactured in week 42 of year 2012 - as rubber degrades over time and also cracks in the tyre tread and side walls. If its beginning to crack (regardless of age) it shows the rubber is passed its best and they WILL be shit compared to how they should perform.