I believe that historically speaking, if means to play the game software/hardware on a console or TV are not available, just about any handheld game that has been a major critical and/or financial success has found its way to consoles either in a port/literal 1:1 conversion or in an "HD" or iterative sequel.

Angry Birds, Tetris, Peggle, Bejeweled, Plants Vs. Zombies, etc. or "portable exclusive" games featuring Kirby, Sonic, God of War, etc. have all been brought to modern consoles ... so, while I'm sure you can cherry pick any portable library for specific titles that have never made it to a full console, when it's warranted via consumer demand and viable to make some money they bring portable games/franchises over.