DS9 episode 'Waltz' (season 6). The main dialogue in the scene starts at about 18 mins 50 secs into the episode (DVD version at least).
Benjamin Sisko: I think something's wrong with the com system. Gul Dukat: Oh ? Benjamin Sisko: It was beeping a second ago. It might need recalibrating. Gul Dukat: I'll check. Everything's fine. The unit's still online. Benjamin Sisko: If you open up the casing you'll be able to run a full diagnostic. Better safe than sorry. Gul Dukat: You're right. Ah. Nothing to worry about, it's working fine. HERE IT IS -> Benjamin Sisko: That's all I wanted to know.
Ideas / opinions for other notable scenes welcome !