What poetic meter is most associated with Shakespeare's plays?

The poetic meter most associated with Shakespeare’s plays is iambic pentameter.

An iamb consists of an unstressed syllable followed by a stressed syllable, as in “to-DAY.” Pentameter means that a line contains five such metrical feet, usually producing a rhythm of ten syllables: da-DUM da-DUM da-DUM da-DUM da-DUM.

Shakespeare used iambic pentameter extensively for heightened dialogue, especially in blank verse, which is unrhymed iambic pentameter. The pattern gives speeches a pulse that resembles English speech while still sounding formal and poetic. Shakespeare regularly varied the rhythm through pauses, inverted stresses, extra syllables, and other effects, so his lines should not be read as mechanically regular.

A useful distinction is that iambic pentameter describes the meter, while blank verse describes unrhymed verse using that meter. Shakespeare’s plays also contain substantial prose and occasional rhymed verse. The form was not invented by Shakespeare: English poets, including Geoffrey Chaucer, used related patterns earlier.