Like most other side-series games, Pokémon Stadium provides, and set the benchmark, various prize Pokémon to be given. These are unlocked through various means and require you to have the Pokémon Green, Red, Blue or Yellow games in the Transfer Pak of the Nintendo 64. Once obtained, you can put them directly into the boxes within Professor Oak's Laboratory

With the Pokémon, if you trade them to Gold, Silver or Crystal at a later point, they will be holding an Item. If obtained in Round 1, they are holding the Normal Box. If obtained in Round 2, they are holding the Gorgeous Box. These boxes, when opened, give access to two new room decorations: The Silver Trophy and the Gold Trophy respectively.

Gym Leader Castle Gift

When you defeat the Gym Leader Castle, defeating the Elite Four and your Rival, you will get a special gift of a Pokémon. These Pokémon are the rare Pokémon of which you get a choice between them within the games. As such, if you don't have access to friends with the games, you may not get. These Pokémon are chosen at random and you can defeat the Elite Four & Rival repeatedly in order to get the Pokémon you desire

Bulbasaur
Level 5
OT:Stadium
ID:02000
Hold Item:
Normal Box
Gorgeous Box
Tackle
Growl
Charmander
Level 5
OT:Stadium
ID:02000
Hold Item:
Normal Box
Gorgeous Box
Scratch
Leer
Squirtle
Level 5
OT:Stadium
ID:02000
Hold Item:
Normal Box
Gorgeous Box
Tackle
Tail Whip
Hitmonlee
Level 20
OT:Stadium
ID:02000
Hold Item:
Normal Box
Gorgeous Box
Double Kick
Meditate
Hitmonchan
Level 20
OT:Stadium
ID:02000
Hold Item:
Normal Box
Gorgeous Box
Comet Punch
Agility
Eevee
Level 25
OT:Stadium
ID:02000
Hold Item:
Normal Box
Gorgeous Box
Tackle
Sand-Attack
Omanyte
Level 20
OT:Stadium
ID:02000
Hold Item:
Normal Box
Gorgeous Box
Water Gun
Withdraw
Kabuto
Level 20
OT:Stadium
ID:02000
Hold Item:
Normal Box
Gorgeous Box
Scratch
Harden
Psyduck

To get the Pokémon Psyduck, you need to register all 151 Pokémon into the Hall of Fame. This is done by winning the various cups or Gym Leader Castle with the Pokémon in your team. As such, this can be very tricky and time consuming to do and due to the lack of Mewtwo as a rental Pokémon, requires a GameBoy game. This Psyduck is special in that it has the move Amnesia, a move which Psyduck cannot normally learn

Psyduck
Level 15
OT:Stadium
ID:02000
Hold Item:
Normal Box
Gorgeous Box
Tackle
Amnesia
Surfing Pikachu

Though not a Pokémon download, there is a special feature when you complete the Prime Cup MasterBall tournament in Round 2. If you defeat the Master Ball division with Pikachu in your team, with it as one of the 3 Pokémon you choose in each of the battles, you will get given the chance to teach Pikachu the special move Surf. This move can only be taught to Pikachu that have been used from Pokémon Green, Red, Blue or Yellow. Pikachu in registered teams or rental Pikachu cannot be used for this.

The Surfing Pikachu can then be used to access a special mini-game within the game Pokémon Yellow