There are many versions of Ganesha, and some substantial artistic differences between geographic areas of Hindu influence. For example, contemporary representations of Ganesha from Nepal are quite different in appearance from Indian representations. There is a spiritual consistency, however, in the various postures, and to be true to the Ganesha traditions there are some clear guidelines.
To quote from http://hinduism.about.com/library/weekly/aa083000a.htm
"Significance of the Ganesha Form
Ganesha's head symbolizes the Atman or the soul, which is the ultimate supreme reality of human existence, and his human body signifies Maya or the earthly existence of human beings. The elephant head denotes wisdom and its trunk represents Om, the sound symbol of cosmic reality. In his upper right hand Ganesha holds a goad, which helps him propel mankind forward on the eternal path and remove obstacles from the way. The noose in Ganesha's left hand is a gentle implement to capture all difficulties.
The broken tusk that Ganesha holds like a pen in his lower right hand is a symbol of sacrifice, which he broke for writing the Mahabharata
. The rosary in his other hand suggests that the pursuit of knowledge should be continuous. The laddoo
(sweet) he holds in his trunk indicates that one must discover the sweetness of the Atman. His fan-like ears convey that he is all ears to our petition. The snake that runs round his waist represents energy in all forms. And he is humble enough to ride the lowest of creatures, a mouse."
Looking at the original subject of this post, there is little in this figure to suggest Ganesha other than the unusual looking "trunk," which is held in the right hand (never a traditional posture for Ganesha). The anomalies here may be the result of a culture long removed from its traditional roots of Hinduism, or perhaps the depiction of a completely different deity, as has been suggested.
Here are two traditional Ganesha forms: