846 of 1025 species can be caught somewhere, across 24 games

The Crown Tundra has the most, 409. PokéAPI holds no encounter records for 8 groups, newer titles mostly.

Game	Gen	Species	Pages
Red and Green (Japan)	I	110	Species list
Blue (Japan)	I	6	Species list
Red and Blue	I	114	Species list
Yellow	I	106	Species list
Gold and Silver	II	164	Species list
Crystal	II	170	Species list
Ruby and Sapphire	III	136	Species list
Emerald	III	158	Species list
Colosseum	III	55	Species list
XD	III	100	Species list
FireRed and LeafGreen	III	157	Species list
Diamond and Pearl	IV	291	Species list
Platinum	IV	290	Species list
HeartGold and SoulSilver	IV	297	Species list
Black and White	V	253	Species list
Black 2 and White 2	V	308	Species list
X and Y	VI	362	Species list
Omega Ruby and Alpha Sapphire	VI	140	Species list
Sun and Moon	VII	246	Species list
Ultra Sun and Ultra Moon	VII	386	Species list
Let's Go, Pikachu and Eevee	VII	128	Species list
Sword and Shield	VIII	381	Species list
The Isle of Armor	VIII	289	Species list
The Crown Tundra	VIII	409	Species list
Brilliant Diamond and Shining Pearl	VIII	0	No records
Legends: Arceus	VIII	0	No records
Scarlet and Violet	IX	0	No records
The Teal Mask	IX	0	No records
The Indigo Disk	IX	0	No records
Legends: Z-A	IX	0	No records
Mega Dimension	IX	0	No records
Pokémon Champions	IX	0	No records