Tends to be walled by Snorlax, Blissey, and Tyranitar, but if you can put them at bay—not easy, but possible—Alakazam will rampage through the rest of the other team. It has many options to attack, support the team, or help itself set up, sometimes all in the same set; Recover ensures that all of these can be pulled off. Another beautiful thing about Alakazam is that it outspeeds Raikou and Starmie. Spikes and poison work well here by putting many things in Psychic 2HKO range. Be careful around potential status afflictions, because any of them (especially paralysis) will seriously compromise his potential.
This is a straightforward attacking Alakazam with some paralysis support thrown in. Psychic and Recover are must-haves, and Fire Punch is nice for Psychic-resistant Steel-types and Exeggutor. You can also use ThunderPunch for the likes of Starmie, Hidden Power Dark for other Psychics in general, or even Ice Punch (though Jynx does Ice/Psychic better). If Alakazam can't smite the opponent with either of its attacks, leave it a nice Thunder Wave to think about. Toxic is a useful alternative here, as it can soften up special walls like Snorlax and Blissey.
While Alakazam is a great attacker, it can also support decently. Alakazam can set up both Light Screen and Reflect for the entire team. Encore is also a great choice to catch Curse users and other set-up Pokémon by surprise and give you free turns to attack or switch. Finally, Counter is a surprisingly delightful choice for a Pokémon with as horrible a Defense as Alakazam. When they attack it for massive damage, it can Counter back for even more massive damage and (more than likely) a KO. If you hit Snorlax with a Psychic on the switch, and use Counter when Snorlax attacks with Double-Edge, you will prevail.
Checks and Counters
Blissey and Snorlax present problems with their good HP and Special Defense, and can easily wear Alakazam down. Blissey can use Toxic or Light Screen, while Snorlax is capable of hitting much harder with Double-Edge or Body Slam.
Dark Pokémon are also good with their immunity to Psychic. They can all potentially carry Pursuit to punish Alakazam for switching out, and Houndoom/Tyranitar can carry Crunch also.
Psychic and Steel Pokémon are viable with a Psychic resistance, but beware of a potentially super effective Fire Punch, ThunderPunch, or Hidden Power.