Sawing a lady in half has been done so often that it is nearly a stereotype. The magician's assistant lays in a box and the magician saws the box in half at the assistant's waistline, inserts two panels to show that the "cut" was successful, and then pulls the two halves apart. This illusion has evolved to include other versions, as when the assistant steps into an upright box, which is divided into three boxes with panels, and the middle box is pulled to the side.
A staple of the great Harry Houdini, the magician is restrained in any number of ways--chains, ropes, straitjackets, etc.--and then immersed in a tank of water, which is also locked. The tank is covered and after a few minutes (or hours) the magician emerges unscathed. This illusion can be done with various sorts of tanks (Houdini sometimes used an oversized milk can), while other magicians prefer to drop the tank in a lake. Another variation includes burying the tank.
The assistant is bound and placed in a locked box. The magician jumps on top of the box, raises a curtain that obscures both he and the box, then shakes the curtain for a few seconds before the curtain drops to reveal that the assistant is holding the curtain. The box is unlocked and the magician emerges. Like the other illusions, this one now includes several variations, as when the magician "reappears" behind the audience and makes a grand re-entrance.
Levitation is always popular but, like the dismembered assistant, has been done so often that it is almost a cliche and is constantly re-invented. The once-simple levitation might now involve multiple objects hovering above the audience or the magician may choose to include himself in the levitation.
Making objects disappear is a favorite of stage magicians. Some seek to make the object as large as possible, as when David Copperfield made the Statue of Liberty "disappear" on national television. Others alter this, making it appear as if the object (or person) was destroyed; one example of this is when the magician appears to cremate his assistant in a coffin on-stage, leaving only a skeleton behind.