-Vaporeon - High Tier
-Availability: Given to you in Celadon City at level 25. You need a Water Stone to evolve Eevee into this.
-Stats: Vaporeon has one of the best stat spreads for in-game use. While its Speed might seem mediocre, it's actually just enough for it to outspeed most of the in-game threats and OHKO them, thanks to its more than adequate Special. If it gets outsped, or if the opponent survives a hit, it won't be taking much damage thanks to its massive HP.
-Movepool: BubbleBeam and Ice Beam (via TMs 11 and 13, respectively) are all it gets in terms of moves when you get it, but that's really all it needs. When you get to Fuchsia, you can teach it Surf as well, but it is recommended that keep Bubblebeam. It also learns Ice Beam by TM and Aurora Beam by level-up (note: it only learns Aurora Beam in Yellow), allowing you to deal with the Bird Keepers without wasting Bubblebeam's or Surf's PP. Keep in mind that BubbleBeam and Ice Beam are both exclusive TMs, and as such Vaporeon might have competition with your other team members. Another thing of note is it's bulky enough to utilize the Rest/Poke Flute combination for (somewhat) reliable recovery.
-Power: From the moment you get it and teach it Bubblebeam, Vaporeon performs excellently against most of its adversaries. In fact, it can take out the Celadon Grunts by itself if you're willing to teach it Ice Beam and use a few Super Potions. After that, Vappy should be caught up with the rest of your team. Unfortunately, the Ghost-types of Lavender Tower are faster than Vaporeon, but it can still do adequately, provided you don't get confused and paralyzed at the same time. From then on, Vaporeon does quite well against most of the remaining trainers, save for the abundant Swimmers late-game.
-Type: Unlike most other Water-types, Vaporeon doesn't have a second type or a move that hurts fellow Water-types effectively, meaning it can't really do much between Fuchsia and Cinnabar.
-Match-ups: Generally, Vaporeon's high HP and Special allow it to perform adequately against the Gym Leaders and Elite Four.
Lt. Surge: If you choose to fight him right after obtaining Vaporeon, don't expect a victory from it, as his Raichu does around half with Thunderbolt, and you have to defeat his Voltorb (which knows Sonicboom) and Pikachu before fighting it. In Yellow, Raichu is his only Pokemon, but its "possible 2HKO" gets bumped up to a "solid 2HKO". In other words, don't use Vaporeon against him, at least not without prior training.
Erika: Her Victreebel/Weepinbell happens to know Razor Leaf, which is almost guaranteed to KO in one hit. However, it is also OHKOed by Ice Beam, so whether Vaporeon or Victreebel comes out alive depends on who's faster. Tangela is more easily beaten, regardless of which game you're playing. Vileplume/Gloom knows Petal Dance, and Vileplume in particular can stomach an Ice Beam. Did I forget to mention Tangela is the only Pokemon of hers that doesn't know Sleep Powder?
Koga: Much more managable than above, thanks to the neutral type match-up, and the fact that his Pokemon have shabby Special. In Yellow, he has 3 Venonats and a Venomoth, all of which are at least level 44 and know status-inducing moves.
Sabrina: Her Pokemon, for the most part, are faster than Vaporeon, but Vappy's great special bulk will allow it to take a few Psychics, along with high HP allowing it to take (seemingly) minimal damage from Psywave. Unfortunately, it can't do too much back, thanks to their high Special. It can still beat at least one of her Pokemon by itself.
Blaine: Literally, the only thing on his team that's actually threatening is Rapidash, and that's only if it spams Fire Spin for about 25 turns.
Giovanni: Provided Dugtrio doesn't spam Sand Attack, you're good to go. In Yellow, his Persian can leave a mark with Slash, and his Nidos know Thunder, but he's still not too threatening.
Lorelei: Don't expect much to come from this fight, as they resist each other's STABs.
Bruno: His Onix are merely speed bumps, and the Hitmons have seemingly no Special. Vaporeon also has enough bulk to take a Hi Jump Kick or Submission if need be, and if it does get hit by Submission, Machamp will lose a chunk of its HP on recoil alone.
Agatha: About her Ghost-types: think of them similarly to Sabrina's Kadabra and Alakazam, except with the threat of status instead of STAB Psychic. Also, the first Gengar knows Mega Drain in Yellow. Aside from that, she's pretty mild.
Lance: All of his Pokemon, barring Gyarados, are OHKOed by Ice Beam, and his Aerodactyl can even be dealt with by Bubblebeam. Vappy also has the bulk to take a non-crit Hyper Beam, but it can't do much to Gyara, and Dragonite knows Thunder (Yellow only) and outspeeds it. Another thing to watch out for is his second Dragonair, as it knows Thunderbolt.
Blue: In Red and Blue, the only ones on his team Vappy shouldn't take on by itself would be Alakazam, Venusaur, and possibly Gyarados. In Yellow, it has a bit more trouble, as Ninetales and Cloyster can continuously trap it with Fire Spin and Clamp, respectively. Also, it is recommended not to have Vaporeon fight Magneton or Jolteon, for obvious reasons.
-Additional comments: From the moment you get it, Vaporeon is a great Pokemon, thanks to its barely-high-enough Speed, high Special, and great endurance. It doesn't even need grinding, thanks to Team Rocket, and it only has 2 problems: While it's effective when fighting most of the Pokemon in the game, it can't really do much to other Water-types not named Gyarados. It's also greatly dependent on BubbleBeam in order to be useful before Fuschia.