Alakazam has the most options of almost any special sweeper in the game. It is one of those Pokemon that can do anything on the special end, and do it well. In addition to strong moves with good coverage, as well as the highest non-Uber Special Attack stat in the game, it has awesome strategic choices such as Encore and Trick, which can completely screw over your opponent for the rest of the match. Alakazam is a force to be reckoned with, and should always be considered when making a team. It does suffer a little from four moveslot syndrome though: it could mess up everything in the game, if only it had more moveslots.
Alakazam does well with a basic Calm Mind set; it has low defenses, but is fast enough to OHKO many Pokémon. Psychic grants it obvious powerful STAB, Fire Punch lets it deal with Metagross, and ThunderPunch helps remove Starmie, Slowbro, and Gyarados. Ice Punch can come in useful against Salamence and Flygon, but a Calm Mind-boosted Psychic takes care of them as well. It's handy for Claydol though. Hidden Power Water is good for the very same Claydol, as well as Houndoom and Tyranitar. Recover is another good move: Alakazam won't be able to use Recover against much, but with a few Calm Minds under its belt, it can handle Ice Beam Blissey, Milotic, and other weak special attackers. Leftovers provides Alakazam with passive recovery, but you might want to use a Lum Berry so freeze and paralysis don't stop Alakazam in its tracks.
Alakazam should always run lots of Speed so it can outrun as many threats as possible and land crucial hits when it needs to. Specifically, maximum Speed lets Alakazam tie with Sceptile and Dugtrio. Other than that, its Special Attack should be maximized as well, because Alakazam's only defense is its offense: KO before it is KOed.
Trick your Choice Band to the Blissey that will most likely switch in, and proceed to destroy it. If you have Recover, you can attack it with Psychic, eventually beating it even if it Seismic Tosses. Substitute lets Alakazam block status effects and Psychic foes until they faint. Furthermore, Substitute enables Alakazam to scout the move of the Choice Band Tyranitar, Snorlax, or Metagross that might come in on it. Macho Brace can be used to screw over fast Pokemon, but it slows down Alakazam before the Trick. You can even use a useless filler item, such as Amulet Coin, and it will work like Thief, but has the extra bonus of allowing Alakazam to swap items with another foe later.
Substitute when you think Blissey will Thunder Wave or Snorlax will Curse, Encore the support move, and proceed to either set up with Calm Mind or attack away. Encore Alakazam is a pain, and it really ruins the likes of Umbreon, who typically has nothing with which to break its Substitute. This variant of Alakazam works well against Celebi too, as it is one of the very few consistently safe switch-ins to a Calm Mind Baton Pass Celebi. Use Recover to make it last longer in such situations.
This physically based Alakazam packs both Focus Punch for the likes of Tyranitar, Blissey, and Snorlax, as well as Trick to cripple unsuspecting special Pokemon. It nearly always works, because these aforementioned Pokemon are the safest switch-ins to Alakazam. Psychic is there for after Alakazam has Tricked away its Choice Band, and it helps by not giving the surprise away too early.
Physical Alakazam needs plenty of Attack investment to make its surprise Focus Punch hurt.
Alakazam also gets access to Barrier, and if you set it up correctly, Alakazam can survive physical attacks enough to make better use of Recover. It's rather risky, though, and needs to be executed flawlessly or it won't work. Thunder Wave can catch Metagross and Tyranitar on the switch and is a nice alternative. Safeguard + Recover enables Alakazam to always beat Blissey one-on-one, and Taunt works against Blissey as well as Celebi. With Knock Off, Alakazam can really hurt the tanking potential of Blissey and Snorlax, and if used on the switch-in, it gives away whether or not your opponent is using Choice Band Tyranitar. Toxic works on just about anything, especially Claydol and Tyranitar.
Checks and Counters
Blissey, the best special wall in the game, is a good initial switch-in to also scout Alakazam's moveset, as she beats most Calm Mind variants—namely, those without Recover. However, watch out for unorthodox moves such as Focus Punch, Trick, and Knock Off, as these will be very annoying. Snorlax takes more damage from Psychic, and unlike Blissey cannot recover health with Softboiled, but he doesn't mind being Tricked a Choice Band as much, and he can usually OHKO or 2HKO Alakazam. If Alakazam carries Recover, Blissey's only way to beat it is with damaging status moves. Thunder Wave will prevent Alakazam from sweeping, but Blissey still won't be able to beat Alakazam one-on-one unless she gets lucky with full paralysis. A badly poisoned Alakazam, however, will eventually faint, and one can always try for the freeze with Ice Beam. The problem with Ice Beam is that Alakazam carries Lum Berry more often than not, which means one will have to freeze it twice. On average, Ice Beam freezes once in 10 turns, and as Ice Beam has a maximum of 16 PP, Blissey will usually lose this matchup unless she has Serene Grace. Note that thanks to Synchronize, if Blissey paralyzes or poisons Alakazam, she will suffer from the same status condition until you switch her out or use Aromatherapy.
Houndoom is immune to Psychic, and—depending on his ability—resists or is immune to Fire Punch. Additionally, he has both Crunch and Pursuit to OHKO Alakazam whether it stays in or switches out. However, if Alakazam has Hidden Power Water or ThunderPunch, Houndoom will be 2HKOed, or even OHKOed if Alakazam has a Calm Mind boost. Tyranitar can use Pursuit as well, and is generally a safer bet as he isn't OHKOed by anything Alakazam can throw at him, doesn't terribly mind being Tricked a Choice Band, and can Rock Slide Alakazam for the OHKO.
Metagross 4x resists Psychic moves and can OHKO with any of Meteor Mash, Shadow Ball, and sometimes even Earthquake. However, he is weak to Fire Punch, making him a shaky counter. While he can survive a Calm Mind-boosted Fire Punch in a pinch, beware of being worn down, burned, or damaged by a critical hit. Jirachi boasts the same typing as Metagross does, and is more durable on the special side. He won't be able to OHKO Alakazam without a novelty move, though, such as Choice Band Shadow Ball or Doom Desire. Celebi resists Psychic, can Recover all day long, and annoy Alakazam with Leech Seed, but it will usually fall to Fire Punch, Ice Punch, Trick, Substitute, or Encore. Claydol makes a good check as long as he avoids a super effective Hidden Power or Ice Punch, as his Psychic resistance, nice Special Defense, and capability to 2HKO with Earthquake or Shadow Ball make him quite a reliable counter.
Dusclops doesn't boast good resistances, but isn't OHKOed by any of Alakazam's moves either, and needs only about 36 Attack EVs to KO Alakazam with Shadow Ball. Sableye is immune to Psychic, can Recover off unboosted hits, and his STAB Shadow Ball KOes Alakazam more often than not. Beware, though, as a Calm Mind-boosted Fire Punch 2HKOes him.