I'd also like to suggest that if I'm using Alakazam in a team battle (doesn't matter with whom) and they have their Pokémon use a special attack, Alakazam can use Psychic on the attack to ensure that it hits the target, similar to a cheap Lock-On.
As for my own team's combos...
Blastoise- Iron Water Spin (Iron Hydro Spin later on): Withdraws into shell, followed by simultaneous usage of Iron Defense, Water Gun/Hydro Pump, and Rapid Spin
Pidgeot- Feather Hurricane: incorporates the Attack lowering feathers of Feather Dance into a Hurricane, causing the attack to both drop the target's attack while damaging
Arcanine- Flare Impact: Covers itself in fire before rushing forward in a Giga Impact. ONLY USED AS A LAST RESORT
Alakazam- Psycho Ball: draws psychic energy from the area around into a tight ball, then hurls it at the enemy
Gengar- Hex Bond: when opponent has status condition, places a Hex and Destiny Bond. ONLY USED AS A LAST RESORT
Persian- Night Screech: lowers opponent's Defense before performing Night Slash