Ray Bradbury's work seems to be quite well known in Russia (and the rest of the former Soviet Union). Several Russian-language films have been based on his works, often without his permission: Vel'd (1987), Trinadtsatyj Apostol (1988), Vino Iz Oduvanchikov (1997).
Two of the short animated films have recently popped up on YouTube. The most interesting of these is There Will Come Soft Rains (1984). In some ways more bleak than the Bradbury original, this film also seems to make some comment on religion, or Christianity, or western values. You can view the film, with English subtitles, here.
Less interesting, and rather primitive in its animation, is Here There Be Tygers. I know very little about this film, except that it is based on the story of the same name (which has been adapted once for live action, in the Ray Bradbury Theater series; Bradbury also wrote a teleplay of the story for the original Twilight Zone series in the 1960s, but it was never filmed). You can view the animated film, with English subtitles, here. Until this version appeared on YouTube, I had never seen a subtitled version; it's nice to be able to understand what's going on in the film!