Well, I think most people would rather interact with something with a human-like personality. Utterly lack of personality in an AI would probably be disconcerting.
As for what they would be like..
I think most of them would have a deep desire to do whatever their function is. If it's a robot designed to run a kitchen, then It would take joy in doing so. AI without functions would probably be depressed and desire for something else to do.
They are made with the purpose of doing something after all, so a certain degree of desire to
do something is expected.
The basic personality they would have would probably be given depending on what they are supposed to do, or on the whims of the programmers. If it's a caretaker AI, then it will probably have a warm, maternal and attentive personality.
Few would have disorganized or chaotic personalities, as for the most part, those would be counterproductive to whatever they are made to do..
Of course, the personality of an AI would probably change over time. Few people would be able to put up with an AI that can't change it's behavior based on events..
“She'd become a governess. It was one of the few jobs a known lady could do. And she'd taken to it well. She'd sworn that if she did indeed ever find herself dancing on rooftops with chimney sweeps she'd beat herself to death with her own umbrella.”
― Hogfather