We present results of the electronic structure and stability of some forty valence electron icosahedral Al12X (X=B, Al, Ga, C, Si, Ge, Ti and As) clusters within the local spin density functional theory. It is shown that the stability of the Al13 cluster can be substantially enhanced by proper doping. For neutral clusters, substitution of C at the center of the icosahedron leads to the largest gain in energy. However, Al12B- is the most strongly bound in this family. These results are in agreement with the recent experiments which also find Al12B- to be highly abundant. {\textcopyright} 1993 The American Physical Society.