Following angevin2's example, I went searching for YouTube links. Alas, the Branagh / Thompson version of this scene seems to have been taken down, but here's the BBC TV version and a Stratford Festival stage production.
Actually, in a lot of ways, this is kind of an aggressively anti-romantic scene, taking place as it does between two people who have spent the first two acts of the play relentlessly mocking the conventions of romantic love, and who have also just witnessed a by-the-book courtship collapse in disaster. And then they're finally left alone, just at the moment when Beatrice is most suspicious of those conventions, furious at the gendered double standards that govern them, and at the same time very aware that she can exploit them to her own ends.
Benedick. Surely I do believe your fair cousin is wronged.
Beatrice. Ah, how much might the man deserve of me that would right her!
Benedick. Is there any way to show such friendship?
Beatrice. A very even way, but no such friend.
Benedick. May a man do it?
Beatrice. It is a man's office, but not yours.
Benedick. I do love nothing in the world so well as you: is not that strange?
Beatrice. As strange as the thing I know not. It were as possible for me to say I loved nothing so well as you: but believe me not; and yet I lie not; I confess nothing, nor I deny nothing.
I love the confusion, the groping, the "believe me not" (and her "why then, God forgive me" a few lines later): she knows what she's about to ask him to do, and she's genuinely afraid that she's not playing fair. But she goes through with it anyway:
Benedick. Come, bid me do any thing for thee.
Beatrice. Kill Claudio.
Benedick. Ha! not for the wide world.
This is such a great moment -- the "oh crap, she actually means it" double-take -- and it's a perfect lead-in to Beatrice's tirade about the worthlessness of men's oaths.
O that I were a man for his sake! or that I had any friend would be a man for my sake! But
manhood is melted into courtesies, valour into compliment, and men are only turned into tongue, and trim ones too: he is now as valiant as Hercules only tells a lie and swears it. I cannot be a man with wishing, therefore I will die a woman with grieving.
One of the big themes in Much Ado is faith -- the characters are so easily led astray by what they see and hear that the senses cannot be trusted. Now, they're groping through the more difficult task of learning to take things on faith.
Benedick. Tarry, good Beatrice. By this hand, I love thee.
Beatrice. Use it for my love some other way than swearing by it.
Benedick. Think you in your soul the Count Claudio hath wronged Hero?
Beatrice. Yea, as sure as I have a thought or a soul.
Benedick. Enough, I am engaged; I will challenge him. I will kiss your hand, and so I leave you. By this hand, Claudio shall render me a dear account. As you hear of me, so think of me.
And so he leaves her with a conventional chivalric gesture -- but this time, there's real substance behind it, and the very real possibility that he may end up getting killed or imprisoned.
As a side note, I really like the way Benedick shifts back and forth between the familiar "thou" and the more distant "you" (Beatrice is always holding him a little at a distance).
Day #1: Your favorite play
Day #2: Your favorite character
Day #3: Your favorite hero
Day #4: Your favorite heroine
Day #5: Your favorite villain
Day #6: Your favorite villainess
Day #7: Your favorite clown
Day #8: Your favorite comedy
Day #9: Your favorite tragedy
Day #10: Your favorite history
Day #11: Your least favorite play
Day #12: Your favorite scene
Day #13: Your favorite romantic scene
Day #14: Your favorite fight scene
Day #15: The first play you read
Day #16: Your first play you saw
Day #17: Your favorite speech
Day #18: Your favorite dialogue
Day #19: Your favorite movie version of a play
Day #20: Your favorite movie adaptation of a play
Day #21: An overrated play
Day #22: An underrated play
Day #23: A role you've never played but would love to play
Day #24: An actor or actress you would love to see in a particular role
Day #25: Sooner or later, everyone has to choose: Hal or Falstaff?
Day #26: Your favorite couple
Day #27: Your favorite couplet
Day #28: Your favorite joke
Day #29: Your favorite sonnet
Day #30: Your favorite single line