Alakazam is based on a magician and the concept of spoon bending. It also shares traits with goats and foxes, both of which animals that have ties to magic powers.
Alakazam could also have drawn influence from sorcerers and/or wizards, which are often portrayed as old, but are considerably smart and powerful. They often utilize powers very similar to those of an average Psychic Type Pokémon.
Alakazam was reputable for being an insanely strong non-Legendary Pokémon, due to the Psychic Type being horribly unbalanced in Generation I. While it does have less than stellar defenses, it's monstrous 135 Special stat, along with excellent speed, enabled it to decimate many opponents in battle.
Alakazam remained viable, even with the introduction of Steel and Dark Types. Alakazam could learn Fire Punch in Generations II and III to deal with most Steel Types, although it would have a hard time dealing with Dark Types, unless one has a Fighting or Bug Type with them.
In Generation IV, when the physical/special split came into play, Alakazam's viability had noticeably suffered, even if it could now learn Focus Blast to deal with Dark Types. Generation V gave it more tools to work with in the form of a Hidden Ability called "Magic Guard", which protects the user from indirect damage, such as Leech Seed, Curse, and weather like Sandstorm or Hail.
In Generation VI, Alakazam was lucky enough to receive a Mega Evolution. While Trace is a rather situational Ability, using it at the right opportunity to copy Abilities like Protean or Magic Bounce, will give Mega Alakazam a great tool in battle if the timing is just right. It can even learn Dazzling Gleam to deal with more Dark Types, in addition to being very handy against most Dragon Types.