They can eat the green tops but not the actual radish
According to Rabbit Welfare it's just the tops:
http://www.houserabbit.co.uk/resources/content/leaflet_pdfs/going_green_oct_06.pdf
Remember, just cos bunnies are shown eating something on TV or in a book doesn't mean it's good for them. Bug Bunny eats carrots all the time but as we know they're sugary and should be given in moderation.