I think that I listened to this song when I was a child – I do not remember, but it somehow got stocked in my mind… And some 25 years later it hit me. Didn’t know the exact lyrics, all I heard was “ochi crushnya”… And if some song hits me, I somehow manage to find what song it is even if I don’t know its lyrics… 
(And without using Shazam, ha!)
So I randomly (:P) searched on Youtube and I think I might have found it listed as suggestion when listening to Kalinka or Katyusha.. Anyway, once I found the title, then the versions obsessed little dwarf on my head activated and .. ta-da, after some digging, I discovered Sophie Milman, a russian-born jazz singer with a divine voice.
Here’s Ochi Chornye by Sophie Milman:
Another great version:
(unfortunatelly unknown credits, I think it might be the St Petersburg Russian Folk Orchestra)
And, of course, the grandious Red Army Choir version:
How about Red Army Choir AND Patricia Kaas:
And this russian song played on a flamenco guitar by taiwanese Ho Lan 