Puzzle Bobble (Game Gear)
Puzzle Bobble (Wonderswan)
Puzzle Bobble (NeoGeo Pocket Color) (at a push, it's called Puzzle Bobble Mini and has different levels so probably doesn't count)
Puzzle Bobble (Gameboy) (also based on newer versions of the game, with route choices etc. same first level as NGPC one)
if anything the above 2 are based on the puzzle mode from Puzzle Bobble 2, at least that shares the same first level
there was also apparently a 3DO port (driver nowhere near good enough) and a N-Gage port (no driver exists)
of course there are a ton of other variations etc. but they stray too far from being 'Puzzle Bobble' to include. You can already see how the ports start to derive from the original, or borrow mechanics from later games in the series due to being released much later.