mobiBLU has introduced what they call the smallest MP3 player. Considering that it measures 24 x 24 x 24 millimeters and weighs 18 grams (about one cubic inch and about 0.64 ounces), they may be right! It features a bright OLED display, supports the MP3 and WMA formats (but not DRM) and includes an FM tuner.
It is available in models with 256MB, 512MB and 1GB of storage capacity.
While not available in North America, a search on eBay will reveal that a few are available.