Mouse as Ganesha vehicle

                                                           

                                              

There are different theories to this:

First, in ancient times, when agriculture was the primary mode of sustenance, rodents were one of the biggest obstacles to prosperity--as they are for farmers even today. Destroying crops, eating stored grains are all in a day's work for a rodent. Lord Ganesha, in having a mouse/rat as his vehicle, is symbolically shown to have conquered this pest, thus staying true to his name and work as the destroyer of obstacles, according to biodiversity of India.

Second, Lord Ganesha was able to reach all the nooks and crannies

 of the world--and do his duty as the destroyer of obstacles--because his vehicle was a mouse--because mice/rats can slither through tiny holes and narrow pathways.

Third,There was a demon (rakshasa) by the name Mushikasura. He was defeated by Ganesha in a battle. The dmon, in order to avoid punishment,offered to be Ganesh's vaahana (vehicle).   

Fourth, The mouse was a celestial musician by the name krauncha. Once, accidentally, he stepped on the foot of sage Vaamadeva who, in turn, cursed him to become a mouse. Krauncha assumed a huge from of mouse and started damaging everything in its path. Lord Ganesha humbled him by catching him in his noose; but before he could punish the mouse, krauncha begged for forgiveness. Consequently, the elephant god made him his vehicle for motion. Since the mouse could not take the weight of Ganesha, the latter reduced his size to accommodate krauncha. Somesay that the name of Ganesha's rat-vehicle is Anindya.