-Mr. Mime - High Tier
-Availability: Obtained from a trade (Abra in RB and Clefairy in Yellow). Its level when you receive it depends on the level of the Pokémon you are trading. Chances are it will be underleveled unless you happen to level up the Pokémon you are going to trade away as you are heading to Vermillion City. However, the boosted experience allows Mr. Mime to gain levels very quickly and it will catch up to the rest of your team in a flash.
-Stats: Mr. Mime has good Speed (90) and Special (100), giving it strong battling capabilities. The HP (40) and Defense (65) are low but it isn’t a crippling problem because most opponents will fold before they strike. Its frailty may come into play in gym leader battle though.
-Movepool: Sadly, Mr. Mime has a poor level-up movepool. Confusion is its only decent attack, although it is acceptable early on and makes a good back-up to Psychic for killing weaklings and conserving PP. Speaking of which, it can learn Psychic through TM, which is pretty much all it needs. It also gets Thunderbolt. Thunderbolt is its best option against other Psychics and it expands its coverage a bit, but it isn't something that Mr. Mime is in desperate need for and it should only be used if you have nothing else to give it to (Electric-types get first dibs).
-Power: Mr. Mime is actually the weakest fully evolved pure-Psychic type, but this is more of a reflection of the quality of the other Psychics rather than Mr. Mime itself. It doesn’t quite OHKO with Confusion like Kadabra/Alakazam tend to but it is still a powerful Pokémon capable of at least 2HKOing pretty much everything. When it gets Psychic (obtainable before Erika) it really takes off and is capable of OHKOing most things.
-Type: Psychic is highly regarded as the best type in RBY. Psychic is super-effective against Fighting and Poison, allowing it to blast through Team Rocket grunts, and it is only resisted by itself so it has excellent neutral coverage.
-Match-ups: Lt. Surge – Decent match-up in RB thanks to high Special and his team's lack of powerful physical moves. Yellow is harder thanks to Mega Punch and Mega Kick. Raichu can take Confusion fairly easily too.
Erika – Psychic destroys almost everything in this whole gym. Tangela can take it better than Gloom/Vileplume and Weepinbell/Victreebel but it can’t do much back.
Koga – Psychic is super-effective against everything and it resists the Psychic attacks being fired back at it in Yellow. It should do great here.
Sabrina – Pretty much a mirror match. The outcome depends on level but Recover gives Kadabra and Alakazam a bit of an edge unfortunately. You should beat Venomoth in RB easily though.
Blaine – This also depends on level but Mr. Mime’s high special helps it take Flamethrower/Fire Blast. It doesn’t dominate because physical attacks hurt but it can contribute.
Giovanni – Psychic makes short work of Nidoqueen and Nidoking. His other Pokémon have poor Special stats but they can hit back hard. Mr. Mime can contribute here too but just be wary of things like Persian's Slash.
Lorelei – A neutral match-up overall, although Slowbro and Jynx resist Psychic so they are tricky to take down (note that Slowbro has Amnesia). Thunderbolt is useful here if you gave it to Mr. Mime, although your Electric type probably got it instead.
Bruno – You win easily here. His fighting Pokémon lose. Onix is frail and can't hit back hard enough to be a real threat.
Agatha – Psychic is super-effective against everything. You should win unless you get unlucky with confusion damage or something.
Lance – There isn’t really an advantage or a disadvantage type wise. Mr. Mime won’t want to take Hyper Beam too much, but it can take special attacks which is handy in Yellow. Thunderbolt is great for Gyarados and Aerodactyl.
Blue – None of his Pokémon are actually weak to Psychic except Venusaur, so this will come down to stats. You should be able to at least beat things like Venusaur, Pidgeot, and Rhydon among others. Thunderbolt will expand your targets too. Overall, Mr. Mime can pull its weight and you just have to pick your targets wisely.
-Additional Comments: Although it doesn't have the raw killing power of Alakazam, it is still a great battler and the massive amount of experience this gains from battling makes it a great choice. It makes Mr. Mime a breeze to train and it also give more opportunities for its teammates to jump into battle and gain experience, making it a great team supporter.