For the pre-selection candidates for the Olympic mascot, see this post.
For the official Sochi Paralympic mascots, see this post.
If you feel nostalgic or hist-curious, here are the pictures of Misha the Bear, the 1980 Moscow Mascot.
Finally, for the satirical mascots of Sochi 2014, click here.
The official mascots of the Winter Olympics in Sochi are:
1) The Leopard (in Russian: Leopard, Леопард)
2) The Polar Bear (in Russian: Belyi Medved’, Белый медведь)
3) The Hare (in Russian: Zaika, Зайка)