Why should an app have a personality? Apps should 'do', not 'be'. In my opinion, the user shouldn't ever notice the interface, because its only purpose is to facilitate the service; anything that disrupts the purpose (like a 'personality') is distracting from what it's supposed to do.

What do you make of a service like Siri that imposes a personality on the UI without disrupting its usability? Anecdotally, many people like communicating with such an interface that simulates human conversation, even if the results themselves aren't improved by it.

Good point. Except for games or kids apps, the ui should get out of the way and have no personality. It should have some identity though, so we can tell apps apart, but a logo and a color scheme is enough usually.