Statistic of using Ukrainian dialect (by yandex.ru, 2010):
As you can see, 80-90% of the people use Great-Russian dialect in everyday situations. Even in such russophobe regions as Ivano-Frankovskaya they use Ukrainian dialect only for 30%.
It's not an official statistic, of course, just for your information.
Also there is an official conclusion of some European commission (I don't remember how it's named), according to the conclusion, Great-Russian dialect is native for more than 80% of the Ukrainian citizens (I don't remember exact numbers, it's something like 83% or 87%).