Drowzee - Mid Tier
-Availability: Drowzee are at Route 11, at levels 9-15 in Red and Blue and at 15-19 in Yellow. The chance of finding them is 1-in-4, so you don't have to worry about scouring the Route for hours on end looking for them. They evolve at level 26, which is when you should be either fighting the last trainers on the S.S. Anne or approaching Rock Tunnel.
-Stats: Unfortunately, Drowzee's uncomfortably slow and (physically) weak. Thankfully, its impressive Special makes up for its Speed somewhat. When Drowzee evolves, it can outspeed most Pokemon in the game that aren't considerably fast (or in the possession of a Gym Leader/Elite Four member). Its Special also gets a nice boost, and its increased Defense means that if it fails to OHKO its opponent (which is a fair assumption considering how late it gets Psychic), it won't have to worry about counterattacks as much.
-Movepool: Unless you're playing Yellow and caught it at level 17 or higher, Drowzee won't know Confusion, having only the pathetic Pound with which to harm others. Headbutt is usable, but is only useful for fellow Psychic-types, as they usually have high Special and resist Psychic-type attacks, not to mention Hypno's Special is far greater than its Attack. Also, Hypno doesn't learn Psychic naturally until level 37, so teaching it that via TM29 isn't completely unreasonable. Drowzee also knows Hypnosis from the moment you catch it, but its unreliable accuracy means that it's far from necessary.
-Power: As mentioned above, Drowzee won't know Confusion until level 17, so until then, it has to 6HKO its enemies with Pound. Once it knows Confusion, it starts to do adequately, and when it evolves, it gets even better, but despite this, its Confusion has a tendency not to OHKO things that aren't weak to it. Psychic, whether it be at level 37 or when you first enter Saffron City, fixes this problem and allows it to deal heavy damage to anything that's not a fellow Psychic-type. Unfortunately, Hypno doesn't do as well as Mr. Mime or Abra in Pokemon Tower, mainly due to it being slower than the numerous Gastly and Haunter, and some of them tend to go for the Confuse Ray on the first turn, and their high Special allows them to survive a Confusion more often than not.
-Type: Psychic is well known for being the best type back in the day, and not having a second type isn't the end of the world, as Psychic-type attacks have great coverage on their own, only being resisted by fellow Psychic-types, who can't do much to Hypno in return.
-Match-ups: While you could just use Hypnosis against everybody, these match-ups will assume you don't use it.
--Lt. Surge: You can handle him in Red and Blue if Drowzee's evolved by this point. In Yellow, however, Mega Punch and Mega Kick leave marks regardless of whether it's a Drowzee or Hypno you're using.
--Erika: Victreebel/Weepinbell is faster than Hypno and can trap it continuously with Wrap. The rest of her team is much easier to deal with, just watch out for Sleep Powder. Getting Hypno statused prior to the battle, which shouldn't be too much of a problem considering the fact that half of the Gym's trainers know status-inducing moves, prevents the threat of Sleep Powder and allows Gloom/Vileplume to be pulverized. Keep in mind that if Hypno gets paralyzed, it's vulnerable to Bind from Tangela.
--Koga: Hypno should have Psychic by this point, but even Confusion has enough power to OHKO his Koffings. Psychic, however, is needed to OHKO his Muk and Weezing, and greatly helps its performance against him in Yellow, although it never really struggles against him in the first place.
--Sabrina: Hypno resists Psychic-type attacks, causing Sabrina's Pokemon to use everything but Psychic-type moves, allowing Hypno to Headbutt them until they're down. Alakazam, though, is a problem, as Recover its its only non-Psychic-type attack, meaning it will endlessly spam it, healing off more than Headbutt will do. There are 2 possible solutions to this, but neither are efficient: the first being to use Disable (which Hypno knows when you catch it) and hope it disables Recover, or to use Meditate (which is learned at level 43) so Headbutt does more than Recover heals.
--Blaine: Fire Spin is annoying, as is Confuse Ray from Ninetales (only appears in Yellow), but Hypno does decently against him otherwise.
--Giovanni: Everything on his team, save for Persian in Yellow and Dugtrio. Hypno can beat them one-on-one, but not both of them in the same match.
--Lorelei: Hypno doesn't do too poorly against her, but Slowbro and Lapras can comfortably take whatever Hypno throws at them.
--Bruno: Ignoring the Onix because they're terrible, Hypno can take on all of his Fighting-types, at least assuming Hitmonchan and Hitmonlee don't use Mega Punch and Mega Kick, respectively.
--Agatha: Her Ghosts and Golbat know Confuse Ray and are faster than Hypno, potentially leading to a very frustrating battle.
--Lance: Hypno can take a Hyper Beam from his Dragonair, but nothing else on his team. As such, Hypno can beat one of his Dragonair, but good luck defeating anything else on his team with it.
--Rival: To make things short: Pidgeot, Rhydon, and Venusaur are easily beaten. Hypno vs. Alakazam results in a stalemate, due to Alakazam's only Normal-type attack being Recover. Exeggutor can be beaten, but it'll take a while. Arcanine, Magneton, Vaporeon, and Jolteon can be troublesome but still manageable provided Hypno doesn't take too much damage against others. Finally, Fire Spin and Clamp make Ninetales and Cloyster infuriating, and Sandslash's, Gyarados's, and Flareon's Attack makes having Hypno fight them inadvisable.
-Additional Comments: Drowzee is a good Pokemon, but one who has competition with Abra and Mr. Mime, the former of which comes earlier and has better stats, and the latter gains boosted exp due to being a traded Pokemon. However, Drowzee is much easier to obtain than its competition, as Abra Teleports away on the first turn and Mr. Mime requires either an Abra or a Clefairy, depending on the version, while Drowzee has a decent chance to appear and it doesn't Teleport away from battle. Of course, its forgettable start also hampers it somewhat, but its solid match-ups against the game's bosses makes up for it.