Come on, you know you know that guy—it's the Cos. Bill Cosby is one of the most often imitated celebrities of our modern era, because he has very recognizable aspects to his speech. Whether or not that's a real part of his speech, a part of his stage speech patterns, or simply something attributed to him through his characters in 'The Cosby Show' doesn't matter—it's completely and instantly known that certain things are imitations of Bill Cosby.
The same thing has to be true if you're going to use character imitation to great effect. This links directly to having totally different, unique speech patterns and pet phrases for each character. If you're going to have characters imitate one another, there has to be something to latch onto.
I remember distinctly one moment in fourth grade (I remember a lot of moments from fourth grade, actually, but one that's applicable.) when we were reading 'The Wanderer.' It was about these people on an old boat or something like that, and it was told through their journal entries. Now, as they grew closer, they started to imitate each other. There was one character that had a habit of repeating things three times (i.e. Bored bored bored.). Late in the book, another character (Looking back, I'm pretty sure they had some kind of budding romance I didn't pick up on as a fourth grader.) starts to do the same thing.
As people get to know others, they pick up on conversational idiosyncrasies—I do it all the time. It makes your characters that much more real, that they are affected by the people around them. Of course, imitation can also be used as mockery—we all know that. But, to do it properly, you still need that uniqueness of speech pattern. Mockery isn't nearly as easy to pull of as books as it is in speech, so you need to really lean heavily on those speech patterns and such.
As far as I'm concerned, imitation and the techniques that go along with it are quite useful, particularly in romantic situations (where two people sort of start to blend personalities) or with younger people, who have a greater tendency to make fun (it's a cliché, but we all know it's still sort of true. We were all teenagers. Remember how it was.).
Now I'm going to go get the pudding...it works better if you can actually hear my voice, I promise...