The border official instead asked me where and with whom I would be staying. I could not tell if she was entering it into the computer or not. She confirmed that immigration cards were not being required here anymore, but wasn't sure it was a permanent change. I kind of suspect it is, since any decision to stop issuing immigration cards requires a corresponding decision to stop requesting them upon departure at every border crossing in Ukraine. This requires top-level planning and establishing a new procedure for entering information in the computer as opposed to storing torn-off scraps of paper somewhere.
At least I'd like to think this is the case and that this isn't something Boryspil airport started doing because their xerox stopped working and they ran out of immigration cards the day I flew in.
UPDATE SEPT. 20, 2010:
We just had a couchsurfer from Moscow at our home. He had to fill out an immigration card at the border. Oh well. So much for consistency of implementation!
UPDATE DECEMBER 2010:
From the news coming in from many different expats it seems that the scrap-paper immigration cards have finally been scrapped for good. Hooray!