Both here and hence pursue me lasting strife,
If once I be a widow, ever I be a wife!
'Tis deeply sworn. Sweet, leave me here a while,
My spirits grow dull, and fain I would beguile
The tedious day with sleep.
Sleep rock thy brain,
And never come mischance between us twain!
Madam, how like you this play?
Queen:Hamlet Act 3, scene 2, 222–230
The lady doth protest too much, methinks.
One of the more interesting quotes by Shakespeare: it's almost always misquoted as "Methinks the lady doth protest too much," Queen Gertrude's line is both drier than the misquotation (thanks to the delayed "methinks") and much more ironic. Prince Hamlet's question is intended to smoke out his mother, to whom, as he intended, this Player Queen bears some striking resemblances [see THE PLAY'S THE THING]. The queen in the play, like Gertrude, seems too deeply attached to her first husband to ever even consider remarrying; Gertrude, however, after the death of Hamlet's father, has remarried. We don't know whether Gertrude ever made the same sorts of promises to Hamlet's father that the Player Queen makes to the Player King (who will soon be murdered)—but the irony of her response should be clear.
By "protest," Gertrude doesn't mean "object" or "deny"—these meanings postdate Hamlet. The principal meaning of "protest" in Shakespeare's day was "vow" or "declare solemnly," a meaning preserved in our use of "protestation." When we smugly declare that "the lady doth protest too much," we almost always mean that the lady objects so much as to lose credibility. Gertrude says that Player Queen affirms so much as to lose credibility. Her vows are too elaborate, too artful, too insistent. More cynically, the queen may also imply that such vows are silly in the first place, and thus may indirectly defend her own remarriage.