The Game Corner has been a staple of every Pokemon game up to Generation IV. Here you can buy coins, test your luck, and win fabulous prizes, including new Pokemon and TMs you won't get anywhere else.
You'll need a Coin Case, to be found in the Goldenrod Underground. At the main desk in Game Corner (in the top left corner) you can buy 50 coins for 1000P or 500 for 10,000P.
Slots and Games
Gold and Silver have two games now. The first is the basic slots game from Red and Blue: insert however many coins you want (1, 2 or 3, which add more rows on the slots where you can win prizes) and try and line up the same picture.
Slots Prize Table:
Three 7's: 300 coins
Three Poké Balls: 50 coins
Three Staryu: 15 coins
Three Squirtle: 10 coins
Three Pikachu: 8 coins
Three cherries: 6 coins
Getting one or two 7's seems to affect the game a little; you might see other Pokemon pop up from time to time to tip the balance of the game if you manage to pull off a 7...
The second game is Card Flip. New to the franchise, Card Flip allows you to pick one or several cards, place a bet on the winning card, and try to win. The less cards you pick the higher the yielding prize.
TM14 Blizzard: 5500 Coins
An frosty blast of Ice-type damage is what you'll get using Blizzard. It's useful against the eighth Gym Leader and the Champion though it has low accuracy so watch out. Blizzard has a modest chance of freezing the opponent.
TM25 Thunder: 5500 Coins
This peal of electrical power will shock the living daylights out of certain Pokemon on Chuck and Pryce's respective teams. To add to the fear factor, Thunder will never miss when it's raining. It also might paralyze the target.
TM38 Fire Blast: 5500 Coins
A decently accurate and extremely powerful Fire-type move, Fire Blast will be immensively helpful in your fights against Jasmine and Pryce. It has a good shot at burning the target.
#023 Ekans: 700 Coins (Gold)
This is the only way to get Ekans in Gold. Pick it up if you like Poison-types or need to complete your Pokedex, but don't expect it to do very much hard work.
#027 Sandshrew: 700 Coins (Silver)
Like Ekans in Gold, Sandshrew can't be caught in the wild in Silver. Sandslash has a bit of muscle behind it so this may be a worthy buy if you like Ground-type Pokemon.
#063 Abra: 200 Coins
Makes catching this little Psychic-type a heck of a lot easier now that he can't escape with Teleport. Evolves into a Pokemon with one of the best Special Attack stats in the game (albeit reaching his last form via trade). If you do use him, your fights against Morty and Chuck might become a lot easier.
#147 Dratini: 2100 Coins.
Extremely rare and learns a myriad of great attacks, Dratini would make a smooth addition to any team. It resists four of the most common Special types and will be a great asset to you later on in the game.
TM32 Double Team: 1500 Coins
Boosts evasion to make the foe's moves miss. This works great both ingame and competitively, though watch out: you may lose all your friends if you try it on them.
TM29 Psychic: 3500 Coins
The most powerful Psychic-type move in the game. It has raw strength behind it and is great for dealing with pesky Fighting-type and Poison-type Pokemon like Hitmontop and Gengar.
TM15 Hyper Beam: 7500 Coins
A very powerful Normal-type move. 150 Base Power, but forces you to recharge after using. Attach it to a fast Pokemon with great Attack power (like Entei) and go hog wild.
#122 Mr. Mime: 3333 Coins
An obscure Psychic-type Pokemon that probably won't be much use to you this late in the game. It has cool Special Attack and Special Defense, but isn't that memorable otherwise. I guess it gets both screen moves which is kind of neat.
#133 Eevee: 6666 Coins
Bill will give you an Eevee anyways, but if you're too lazy to breed that one you can get a healthy Eevee for an easy 6666 coins in Celadon City. Remember that it can evolve into five Pokemon now: the types it can take on include Fire, Water, Electric, Psychic and Dark.
#139 Porygon: 9999 Coins
Exclusive to the slots, Porygon is very expensive. If you're looking for a strong battler, it's not going to be Porygon, though it has a fun novelty to it you could try and make work with its neat movepool. Get the Upgrade though from Silph Co. and you can have some interesting battles using Porygon2.