Beg, entreat, beseech, implore, supplicate, adjure, importune mean to ask or request urgently.
Beg suggests earnestness or insistence especially in asking a favor.
Entreat implies an attempt to persuade or to overcome resistance in another especially by ingratiating oneself.
Beseech implies great eagerness and often anxiety or solicitude.
Implore, often used interchangeably with beseech, at times suggests even greater urgency in the plea or more manifest anguish.
Supplicate adds to entreat the suggestion of fervent prayer or of a prayerful attitude.
Adjure implies an injunction as well as a plea and is strengthened by the expressed or implied invocation of a sense of responsibility or duty or of something sacred. It may sometimes suggest little more than urgency or peremptoriness.
Importune commonly suggests repeated attempts to break down resistance and often connotes annoying pertinacity.