gotta catch 'em allDo you want to catch a Vaporeon in one of your Pokémon games? Of course you do! So here's how! Just as a note, Vaporeon appears in a number of spinoff titles, like the Mystery Dungeon and Pokémon Ranger series, but I'll be detailing the main Gameboy/DS games here only. 'Cause I only really play those.
Red, Blue, Yellow, LeafGreen, & FireRed In the first three games for the Gameboy and Gameboy Color and the Gameboy Advance remakes, Vaporeon can be obtained through the Eevee found in the Celadon Mansion, in a Pokéball on the fourth floor at level 25. Water Stones can be purchased at the Celdon Department Store for 2,100 dollars (or whatever the currency is. Pokédollars?).
Gold, Silver, & Crystal In the second set of Pokémon games for the Gameboy Color, an Eevee is obtained from Bill in Goldenrod City after he fixes the Time Capsule. In Gold and Silver, Eevee can also be bought at Celadon's Game Corner for 6,666 coins. Water Stones are a bit hard to come by in Gold and Silver, only obtainable from Mystery Gift, an item on Route 25, or by showing Bill's grandfather at Cerulean Cape a Staryu when he asks for one. In Crystal, additional Water Stones can be obtained from Fisher Tully on Route 42.
Ruby, Sapphire, & Emerald Vaporeon is sadly unavailable in-game in the third series of Pokémon games for the Gameboy Advance. Lame! No wonder I never liked these games. You'll have to trade an Eevee in from FireRed, LeafGreen or from the Pokémon XD Gamecube game. A Water Stone can be found in the Abandoned Ship or through giving Blue Shards to the Treasure Hunter on Route 124 near Mossdeep City. Blue Shards can be stolen from or found on wild Clamperl or found underwater.
Diamond, Pearl, & Platinum In the fourth set of games for the DS, there are multiple ways to get Vaporeon. An Eevee is obtained from Bebe in Hearthome City after completing the National Dex in Diamond and Pearl or after simply reaching the city in Platinum. Eevee can also be caught (for the first time!) in the Trophy Garden after talking to Mr. Backlot (tip: you can save and reset in front of him until he talks about the Pokémon you want appearing in the garden). Water Stones can be dug up in the Underground.
HeartGold & SoulSilver Vaporeon is obtained in the same manner as the original Gold and Silver; Bill gives the player one after speaking to him in his house in Goldenrod City. Fortunately, Water Stones are easier to come by in these remakes. They can be obtained as a prize for winning first place in the Bug Catching contest or bought from the Salon Shop at the Pokéthlon Dome for 2500 points on Monday, Tuesday, Wednesday, or Friday (after getting the National Dex). You can again receive one from Bill's grandfather, this time by showing him a Staryu or a Marill, and Fisher Tully will also give them to the player should you register his number in the Pokégear. A Water Stone can also be found in the Seafoam Islands.
Black & White Eevee is unobtainable in the fifth generation games, sadly, so you'll have to trade one over from the fourth generation games. Water Stones can be found in Castelia City, given to the player by a man on the pier, and Driftveil City near the lighthouse. They can also be bought in Black City or found in White Forest, depending on which version you have. With the release of Black and White there also came something called the "Dream World," which players can access on the internet. While in the Dream World, a player can befriend different Pokémon, some of which will have a unique Hidden Ability. Vaporeon's is Hydration.
X & Y Eevee can be caught on Route 10 or in a Normal type Friend Safari. Water Stones can be obtained on Routes 8, 12, and 18 or purchased at the Stone Emporium in Lumiose City.