@Iced Coffee rewards of completing the Pokedex
RGBY: Diploma (You can print the diploma in Yellow due to being compatible with GB printer)
GSC: Another diploma (and still can be printed)
RSE: 2 diplomas for completing the regional and national pokedex + chosing one of the Johto starters by completing the regional one (only in Emerald).
FRLG: 2 more diplomas.
DPPT: 2 more diplomas.
HGSS: 2 more diplomas + a trainer card star.
BW: 2 more diplomas + trainer card star.
B2W2: 2 more diplomas, access to the Nature Preserve in where you find a shiny Haxorus (you only have to see all Pokemon for this one), a oval stone to increase the rate of founding eggs in the daycare and a shiny charm that makes more common finding shiny Pokemon.
XY: 2 more diplomas, oval stone and shiny charm.
ORAS: 2 more diplomas, medals, oval stone and shiny charm.
SM: the diplomas are replaced for a stamp in your passport + a shiny charm.
USUM: Stamp, shiny charm and a karate gi that your character can wear.
LGPE: the shiny charm only.
SwSh: the diplomas are now a certificate + a shiny charm.
BDSP: The diploma returns, and get a shiny charm and capture charm to increase the chances of a critical capture.
Legends Arceus: Shiny charm.
SV: Diploma, shiny charm and a beast ball to catch ultra beasts. TTM DLC gives a glimmering charm that increases the ammount of tera raids and TID DLC gives a Mark charm to increase the rate of finding Pokemon with marks
Z-A: 1000 research points.
This don't include spin-offs.