Scyther
A moveset consisting of Swords Dance, Aerial Ace, Quick Attack and Brick Break is almost unstoppable in Little Cup, with no Pokémon in Little Cup able to resist that attack combination. Both Aerial Ace and Quick Attack have their power boosted by 50% due to Technician, the latter attack is vital in stopping Pokémon using Choice Scarf to outspeed it or in stopping slower users of priority attacks. Scyther's pedigree is enhanced by the sheer power of its Base Stats, boasting both the second highest Attack stat, base 110, and the second highest Speed stat, base 105.
Sneasel
Sneasel can run a similar moveset to Scyther consisting of Swords Dance, Ice Shard, Bite and Brick Break and be equally difficult to stop. Also akin to Scyther, it boasts a priority attack and an attack combination that no Pokémon resists. With a 95 base Attack stat and the highest unboosted Speed in Little Cup with a base stat of 115 makes Sneasel all the harder to stop.
Yanma
Already in one of the highest Speed tiers, Yanma's Speed Boost ability means that after two turns it will outspeed virtually everything. From there it can wreak havoc with STAB Air Slash or STAB Bug Buzz from a respectable Special Attack stat or simply put to sleep anything it can't kill with Hypnosis.
Tangela
With Sunny Day in effect, Tangela becomes an offensive juggernaut. Its Chlorophyll ability can take its Speed stat to 30 and it can power through anything not resistant to Grass-type attacks with SolarBeam from a 100 base Special Attack stat, who not even Munchlax can stand up to when factoring Life Orb in. Hidden Power Fire and AncientPower provide it with good type coverage or it can take the option of putting its counters to sleep with Sleep Powder. Moreover, Tangela's bulky defensive nature -- in particular its 115 base Defense stat -- makes it even harder to take down.
Meditite
Pure Power transforms Meditite into a very potent threat, reaching 28 Attack with no item boosts, not even Cranidos and its 125 base Attack stat can match that. Hi Jump Kick, Psycho Cut and Ice Punch gives it all the coverage it needs, and such is the power of Hi Jump Kick is that with Life Orb it can OHKO Bronzor, arguably the best defensive Pokémon in Little Cup, who is not even weak to it. Alternatively, Choice Scarf can be used to remedy its average Speed stat and make it difficult to revenge kill. It is very possible that Meditite will be tested again in the future, though.
Murkrow
Murkrow was allowed in Little Cup for longer than the rest of the banned Pokémon but in the end it was deemed that its ability to sweep through multiple members of a team without any set-up pushed it over the banned threshold. Sucker Punch really makes Murkrow difficult to take on, bypassing the speed hierarchy with an 80 Base Power STAB attack with priority running off 91 base Speed (i.e. the second highest speed tier aside excluding Sneasel and Scyther). Pluck complements Sucker Punch and runs off its 85 Base Attack, and hits any Pokémon carrying a berry, such as the Oran Berry, favored by walls, for 60 Base Power (90 Base Power after STAB), disabling and consuming the berry in the process. Dark Pulse hits many physical walls, such as Gligar and Koffing for plentiful damage and has a 20% flinch rate. Murkrow also has access to Hidden Power, Heat Wave, Calm Mind and Pursuit. Murkrow was not unstoppable but was deemed too powerful and was also a clear centralizing force.
DeepSeaTooth
Clamperl is not banned, but the DeepSeaTooth item is. DeepSeaTooth can give Clamperl up to 36 Special Attack, more than a Modest Choice Specs Abra, whilst still retaining freedom to switch attacks. Surf, Ice Beam, and Hidden Power Electric or Hidden Power Grass provide good coverage and not even Munchlax, the Pokémon widely considered to be the best Special wall in Little Cup, can switch in on Surf, being 2HKOed, even taking Oran Berry into account. Its low Speed is a problem but if it is Baton Passed an Agility then it will be incredibly dominant over an opponent's team. Without DeepSeaTooth, however, Clamperl is much more manageable.