I am not a fan of playing on mobiles personally but beside the many crap titles there are a few nice ones that spawned game characters that are not super shallow. The start of this probably growing list made Ceodore Harvey, one of the protagonists in Final Fantasy IV: The After Years that was first released for mobiles before it made its way to the Wii, PSP and other platforms.  

Ceodore Harvey

Ceodore Harvey

Gekkou

Gekkou

Harley (FFIV)

Harley

Izayoi

Izayoi

Jacob Taylor

Jacob Taylor