Personally I think the ability to improvise is absolutely critical for all musicians, especially pianists, who far too often are not asked too in the classical genre--just because there's a whole repertoire of masterpieces doesn't mean one can't make up a new one on the spot! In my opinion, it shows a thorough knowledge of the repertoire and the styles, and the ability to think creatively and access the diverse capabilities of the instrument. I recently underwent a temporary teacher change, and my piano instructor for this term started off the first studio class by having us all get up on stage to take turns improvising, after he found that few people had pieces ready to play in class (it was week 1, so of course everyone was still working on their pieces). It was very enlightening--many of the 'virtuosi' in the studio played quite conservatively in their improvisation, while the people who have struggled a bit more to constantly put out repertoire at a high level really shined when given the opportunity to improvise.
Somehow, I think it follows one's musical personality--if one is more inclined to a judging, analytical approach to life (including music), repertoire will be easier, but it will be very tricky to get truly comfortable playing on stage without a predetermined plan; on the other hand, someone who is very spontaneous in life and in music often has great difficulty in playing a piece consistently well, since they can "get a wild hair" on the performance stage and occasionally make mistakes that would be avoided by more calculated preparation and performance; but in improvisation, this "wild hair," also known as inspiration, or even 'genius,' is the very essence of the music, and it fits around the pianist's own technical preferences and musical tastes, rather than the composer's.