Wikipedia has this typology of magical techniques. Of course, many magical routines use combinations of effects. Here they are:
Production The magician produces something from nothing—a rabbit from an empty hat, a fan of cards from thin air, a shower of coins from an empty bucket, or the magician themselves, appearing in a puff of smoke on an empty stage — all of these effects are productions.
Vanishing The magician makes something disappear—a coin, a cage of doves, milk from a newspaper, an assistant from a cabinet, or even the Statue of Liberty. A vanish, being the reverse of a production, may use a similar technique, in reverse.
Transformation The magician transforms something from one state into another—a silk handkerchief changes colour, a lady turns into a tiger, an indifferent card changes to the spectator’s chosen card. A transformation can be seen as a combination of a vanish and a production.
Restoration The magician destroys an object, then restores it back to its original state—a rope is cut, a newspaper is torn, a woman is sawn in half, a borrowed watch is smashed to pieces—then they are all restored to their original state.
Teleportation The magician causes something to move from one place to another—a borrowed ring is found inside a ball of wool, a canary inside a light bulb, an assistant from a cabinet to the back of the theatre. When two objects exchange places, it is called a transposition: a simultaneous, double teleportation.
Escapology The magician (an assistant may participate, but the magician himself is by far the most common) is placed in a restraining device (i.e. handcuffs or a straitjacket) or a death trap, and escapes to safety. Examples include being put in a straitjacket and into an overflowing tank of water, and being tied up and placed in a car being sent through a car crusher.
Levitation The magician defies gravity, either by making something float in the air, or with the aid of another object (suspension)—a silver ball floats around a cloth, an assistant floats in mid-air, another is suspended from a broom, a scarf dances in a sealed bottle, the magician hovers a few inches off the floor. There are many popular ways to create this illusion of even the magician himself being levitated.
Penetration The magician makes a solid object pass through another—a set of steel rings link and unlink, a candle penetrates an arm, swords pass through an assistant in a basket, a saltshaker penetrates the table-top, a man walks through a mirror. Sometimes referred to as “solid-through-solid”.
Prediction The magician predicts the choice of a spectator, or the outcome of an event under seemingly impossible circumstances—a newspaper headline is predicted, the total amount of loose change in the spectator’s pocket, a picture drawn on a slate. Prediction forms the basis for most “pick-a-card” tricks, where a random card is chosen, then revealed to be known by the performer.